According to John Chancellor, in his book The Flowers and Fruits of the Bible (NY: Beaufort Books, Inc., 1982, p.42), the lily (actually "lilies of the field") Jesus spoke of in Matthew 6:28-29 was the poppy anemone (Anemone coronaria). Chancellor is a noted biographer (his subjects included Darwin, Richard Wagner, John James Audubon, and King Edward I.
[from dust jacket of his book:] Chancellor is a keen gardener and has a remarkable collection of early botanical books which includes some of the flora of the Holy Land.
Chancellor goes on to say,
"Certain alternatives to the poppy anemone have been proposed. One is the white-rayed chamomile, Anthemis palaestina of the Compositae family. The charm of this daisy-like plant became obvious only at the time of hay-gathering which might have illustrated our Lord's point more effectively than the showy poppy anemone.
Another is the glorious scarlet poppy, Papaver species of the Papaveraceae family. The poppy anemone, Palestine anemone or windflower, to give some different names for Anemone coronaria, covers the ground with brilliant blossom in early spring. It is the most conspicuous of all spring flowers. Walking at this season in the Holy Land, among the olives and through fields of thisles and wild grass, I was often hit by an unexpected flash of red--it was the anemone, the "lily of the field" of our Lord's discourse.
According to editors Louw and Nida, as cited by the NET Notes here,
Though traditionally κρίνον has been regarded as a type of lily, scholars have suggested several other possible types of flowers, including an anemone, a poppy, a gladiolus, and a rather inconspicuous type of daisy” (Greek-English Lexicon of the New Testament Based on Semantic Domains. New York, NY: United Bible Societies, 1988).
The NET Notes conclude in footnote 38,
In view of the uncertainty, the more generic “flowers” has been used in the [NET] translation.
Interestingly, commentator Constable in his "Notes" (found in the NET Bible here) says this:
The lilies of the field were probably the wild crocuses that bloom so abundantly in Galilee during the spring. However, Jesus probably intended them to represent all the wildflowers. [my italics]
According to The Trees, Plants, and Flowers of the Holy Land, the anemone has traditionally been identified with Jesus' "lilies of the field":
Green hills adorned with thousands of crown anemones announce spring’s arrival. The flower blooms from December to April. Although blue, white, purple, and pink anemones exist, red is by far the most common. The anemone typically has six petals which close in the evening and reopen with the morning light. Traditionally, these are the lilies of field to which Jesus compares Solomon in all his glory (Matt 6:28, Luke 12:27).
According to Gill's Exposition of the Whole Bible, as quoted here,
. . . [Let us] consider the lilies of the field or "the flowers of the field", as the Arabic version reads it, the lilies being put for all sorts of flowers. The Persic version mentions both rose and lily; the one being beautifully clothed in red, the other in white. Christ does not direct his hearers to the lilies, or flowers which grow in the garden which receive some advantage from the management and care of the gardener; but to those of the field, where the art and care of men were not so exercised: and besides, he was now preaching on the mount, in an open place; and as he could point to the fowls of the air, flying in their sight, so to the flowers, in the adjacent fields and valleys: which he would have them look upon, with their eyes, consider and contemplate in their minds, how they grow; in what variety of garbs they appear, of what different beautiful colours, and fragrant odours, they were . . ..
With the picture in our minds of Jesus pointing--while he is talking--to the birds flying nearby, or the flowers growing in the fields near to where he delivered his "Sermon on the Mount," the bright red crown anemone would certainly provide a readily available visual aid!
According to Robertson, in his Word Pictures of the New Testament, quoted here,
The lilies of the field (τα κρινα του αγρου — ta krina tou agrou). . . . may include other wild flowers besides lilies: blossoms like anemones, poppies, gladioli, irises (McNeile).
According to McGarvey and Pendleton, authors of the Commentary on Matthew 6:28 in their "The Fourfold Gospeland quoted here,
Which lily is here meant cannot be determined. Calcott thinks it was the fragrant white lily which grows profusely all over Palestine. Smith favors the scarlet martagon; Tristam, the anemone coronaria; and Thomson, the Huleh lily, a species of iris. It is likely, however, that scholars are trying to draw distinctions where Jesus himself drew none. It is highly probable that in popular speech many of the common spring flowers were loosely classes together under the name lily. [my emphasis and italics]
[When] Jesus said, ‘Consider the lilies.’ If He were no more He would still be not only the greatest of religious teachers, but quite alone in the character of His teaching. Jesus Christ, amid the awful things of time and eternity, taught man, as none other did, the lessons of the impulses of nature. He bade us be not too busy to consider the fowls of the air and the lilies of the field. He was really interested in such things; they were not to Him the material for rhetorical phrase-making. He said, ‘Your heavenly Father careth for them.’ To the mind of Jesus, and therefore to the mind of God which He declared unto us, beauty was a sacred thing. It was His Father Who spread the Galilean fields with a carpet more splendid than the robes of Solomon. No wonder, then, that He recognised and bade men ponder well their loveliness. Gazing upon their sumptuous beauty, He was glad because these gifts to the humblest outshone the pomp of kings. [my emphasis and italics]
In other words, Jesus, in addressing an audience composed primarily of common, ordinary, working-class people, illustrates and underscores the point he is making by drawing their attention to a common, ordinary, and perhaps even taken-for-granted flower. He then uses logic to drive home his point that working-class people need not succumb to cares, worries, and anxieties.
According to Nisbet, in a sermon entitled "Lessons from Lilies," found in his Church Pulpit Commentary, and quoted here, he encourages his readers to "consider the lilies," just as Jesus suggested in Matthew 6:28 -
Jesus said, ‘Consider the lilies.’ If He were no more, He would still be not only the greatest of religious teachers, but quite alone in the character of His teaching. Jesus Christ, amid the awful things of time and eternity, taught man, as none other did, the lessons of the impulses of nature. He bade us be not too busy to consider the fowls of the air and the lilies of the field. He was really interested in such things; they were not to Him the material for rhetorical phrase-making. He said, ‘Your heavenly Father careth for them.’ To the mind of Jesus, and therefore to the mind of God which He declared unto us, beauty was a sacred thing. It was His Father Who spread the Galilean fields with a carpet more splendid than the robes of Solomon. No wonder, then, that He recognised and bade men ponder well their loveliness. Gazing upon their sumptuous beauty, He was glad because these gifts to the humblest outshone the pomp of kings.
According to Henry Alford, in his commentary on Matthew 6:28, quoted here,
[Consider (Gk.] καταμάθετε), implying more attention than ἐμβλέψατε: the birds fly by, and we can but look upon them: the flowers are ever with us, and we can watch their growth. These lilies have been supposed to be the crown imperial, (fritillaria imperialis, κρίνον βασιλικόν, Kaiserkrone,) which grows wild in Palestine, or the amaryllis lutea, (Sir J. E. Smith, cited by F. M.,) whose golden liliaceous flowers cover the autumnal fields of the Levant. Dr. Thomson, “The Land and the Book,” p. 256, believes the Huleh lily to be meant: “it is very large, and the three inner petals meet above, and form a gorgeous canopy, such as art never approached, and king never sat under, even in his utmost glory. And when I met this incomparable flower, in all its loveliness, among the oak woods around the northern base of Tabor, and on the hills of Nazareth, where our Lord spent His youth, I felt assured that it was this to which He referred.” Probably, however, the word here may be taken in a wider import, as signifying all wild flowers. [my emphasis and italics]
According to the comments of Heinrich Meyer, from his Critical and Exegetical Commentary on the New Testament, and quoted here,
κρίνον, שׁוּשָׁן, lilies generally, various kinds of which grow wild in the East, without cultivation by human hands ( τοῦ ἀγροῦ). There is no reason to think merely of the (flower) emperor’s crown (Kuinoel), or to suppose that anemones are intended (Furer in Schenkel’s Bibellex.); the latter are called ἀνεμῶναι in Greek. . . . The plurals ( αὐξάνουσιν, etc., see the critical remarks) describe the lilies, not en masse, but singly (Kühner, ad Xen. Mem. iv. 3. 12, ad Anab. i. 2. 23), and indeed as though they were actual living persons (Krüger on Thuc. i. 58. 1). Comp. in general, Schoemann, ad Isaeum ix. 8.
And finally in my list of citations is an excerpt from the Cambridge Greek Testament for Schools and Colleges, cited here,
τὰ κρίνα τοῦ ἀγροῦ, identified by Dr Thomson (Land and Book, p. 256) with a species of lily found in the neighbourhood of Hûlêh. He speaks of having met with ‘this incomparable flower, in all its loveliness … around the northern base of Tabor, and on the hills of Nazareth, where our Lord spent His youth.’ Canon Tristram (Nat. Hist. of the Bible) claims this honour for the beautiful and varied anemone coronaria. ‘If in the wondrous richness of bloom which characterises the Land of Israel in spring any one plant can claim preeminence, it is the anemone, the most natural flower for our Lord to pluck and seize upon as an illustration, whether walking in the fields or sitting on the hill-side.’
Tentative Conclusion to the Question at Hand
So we have come full circle to the likelihood that the "lilies" to which Jesus referred could very well have been the anemone coronaria, though there is nothing wrong with the English translation, lilies, since virtually any flower of the field has a unique beauty, regardless of its taxonomy (i.e., the term for the various heuristics for plants, which includes kingdom, phylum, class, series, family, genus, and species).
Furthermore, the experts seem to be agreed in asserting that the exact species of flower Jesus may or may not have been referring to in his illustration is relatively unimportant. Even if we were to know conclusively the flower was this or that species, the far more important part of Jesus' teaching addresses the common human foible of being weighted down with care about where his followers' next meal is coming from or how they can afford to clothe themselves.
The more important point is this: God the Father empathizes with his children in their common cares and anxieties, and proof of that can be found in his provision for lesser important things such as birds and flowers. As to the reasoning behind Jesus' illustrations in Matthew 6:25-34, and the application of those illustrations to the everyday life of his disciples, Jesus used the argumentum a minore ad maius).
The "argument" goes as follows: If God lavished so much beauty and creativity on something as insignificant as a flower, whose beauty lasts but a few short days, how much more love and concern will he lavish upon his children who were created in his image by providing them with clothes to wear.
I use the word concern deliberately, because anxiety, a kissing cousin of concern, is the root problem Jesus addresses at this point in his Sermon on the Mount.
The lilies of the field and the birds of the air have no worries. God clothes the fields with beautiful lilies by providing them with all they need: seeds, soil, sunshine, and water. He also feeds the birds of the air with tiny morsels of food which, not so coincidentally, often come from the flowers of the fields.
If, then, he does these things for mere flowers and birds, why would he not do the same thing for his children who are created in his image? The answer, of course: He wouldn't!