When dealing with James, my amateur opinion is that much can be made of reading the entire context of James.
First, we can refer immediately to the preceding verse, 1:10. James is writing about the rich person, singular: ploucioc / G4145.+
As Noam Sienna answered, correctly, the reference of the fading flower is to mortality. Because 1:10 named a singular individual, the rich person who dies, the flower, which falls from the grass, is singular. The two words are connected by the metaphor.
That is, my answer to the question: "Why is James 1:11 phrased awkwardly, with a singular flower per grass?" My answer would be, "because the fading flower is in analogy to the attractive appearance of the individual rich person from the preceding verse."
What James means by the euprepia, "good-conspicuity" or "good looks" of the rich is also described in James in Chapters 2, and 5, especially 2:2-3, and 5:2-3. In Chapter 2: James 2:2, the rich man has the description: "xrucodaktulioc en estheti lampra"/"gold-ring-wearing; in clothes splendid." So the description of the rich individual in James 2:2 is one who is distinguished by that person's appearance.
Read James 2:1-2:10 for a very long section on the rich, which includes 2:2 and 2:3 mentioning appearance (nice clothes, gold ring) specifically.
Note also James 5:1-5:6, in which James addresses the rich directly. This is my English cribbing of it:
Attention now, rich people: You lament and howl for the judgements that are approaching you.
The riches of you have rotted and the garments of you, food to moths have become.
The gold of you and the silver of you corroded; and the venom of them, into witness of you shall be; and they shall be (ravenously) eating the dead flesh of you, as fire you accumulate in last days.
["as fire" above means "as if the gold and silver were fire" but the Greek doesn't have all those extra words.]
Be perceiving, the wage of the workers: the ones mowing the fields of you, the ones having been deprived by you, ([the wage]) is crying and the implorings of those reaping into the ears of Lord Sabaoth have entered.
You luxuriate on the land and you squander. You nurture the hearts of you, as in the day of slaughter.
You convict, you murder, the Righteous One. Not he is resisting to you.
[No longer is James addressing the rich, but now the poor:]
Be patient, then, my brothers, for the coming of the Lord...
So you can see from this that James thought a few things about the rich. In James 5:1-6, what relates directly to James 1:11 are the following concepts:
James 5:2 is specifically about the clothing of rich people. Both James 5:2 and 5:3 relate to gold and silver, which is consistent with the gold ring of James 2:2. However, I would submit that they mean something else.
James 5:1,3, and 5, are all about how the death of rich people.
James 5:7 is also about the reaping of the rich people. The first and second rain refer to Elijah, just as James 5:17 mentions the story of Elijah and the priests of Baal. Together these (5:7, 5:17) clarify that the 5:7 reference to early and late rain is a reference to people being killed by Yahweh. So 5:4, 5:7 make it clear that there will be a "wage" to be paid for the sin of the rich (exploitation of the poor), and that the usual wage of sin, death, will be charged.
In this regard, 5:7 is a continuation of the "fields" metaphor. However, by 5:7, 5:17-18, James is writing about circumstances after the return of Christ. Thus, xorton ("field") is no longer the word for field, but gec ("land"). James is like that. The rich person was a grass with a pretty flower, but the land-acter's (farmer's) harvest in 5:7, 5:18 is karpon. Both the same word for land-acter and the word for fruit are repeated between 5:7 and 5:18, more firmly making the connection.
These uses of the word karpon for "fruit" relate back to 1:18, where he uses "aparxen" to mean "first-fruit." For James, the fruit harvest of the Lord, that consisting of the souls of mankind, is of course the subject of eschatological and genesiological commentary.
I'll update you someday on the rest of the answer. At the moment, I can say that the "rich" whom James addresses were probably those whom he encountered locally. Thus, I believe his address to his brothers about the rich, and finally to the rich in 5:1-6, is to be considered in terms of the problems he saw with the local rich. James complaints were several, but he specified at least these: employment practices (or pay practices), relaxation while others worked, that they received special dispensations by virtue of wearing expensive adornments and clothes, and a few other things that will have to come with the update. I just wanted to put this out here while I saw the question today.
Finally, here is a response to something you asked: I haven't considered that the metaphor of the flower might be related to the "heat" of the rich as you ask. I consider your idea a blessing although I do not yet concur with it.
I hope you now see that James made a few references to the appearance of the rich. My conclusion is that he was emphasizing that the trappings of wealth are mostly superficial. However, he did directly address the practical differences with regard to those who labor in fields and those who relax while owning those same fields. So while his complaints with the rich were somewhat detailed, or deep, his description of them was repeatedly superficial.
In 2:2-3 he is clearly talking about a situation from his time: a rich person being recognized as rich and afforded status due to a gold ring and splendid clothing. It's key to realize that the clothing and the appearance would be the way most of James' listeners would recognize rich people when they saw them.
The appearance of the rich is the first thing James analogizes with death and decay, James 1:10-11. I imagine this is because James wanted to address any covetousness among his brothers by writing 1:10-11 to them.
I would also like to broaden your question slightly further to James 1:9. In my view, at least 1:9-11 must be read together. James does not believe that any person who profits (see also, James 4:13-17) is a sinner; not at all. On the contrary, it's the lazy, exploitive, etc., rich who have it coming, and the brother who profits does so at the mercy of the Lord. That is to say, sometimes Christians make money. James has specific complaints about the rich.
1 Note that I consider myself an amateur James lover moreso than a person knowledgeable in Koine generally. And I must mention that it is my personal translation of "euprepia", Strong's G2143, as "good conspicuity," in this case from James 1:11 specifically. A more detailed translation in this verse might be "the good looks" or "the good appearance."
2 Someone can supply the Greek, I hope, because apparently I don't do Unicode today. I created my account to answer, but I apologize for not prettying up my Greek. I don't want to pretend Greek is my thing. Also, the original MSS have no breathing marks, that I am aware of. So I like to skip those entirely. I like a major uncial script. But that's me.
3 I take G5004 rather poetically here, because I prefer to think James was rather a poet in Greek. That is, G5004 is compounded from "scales (balances)" and "trials," meaning "calamities." I go so far as to believe James intended to use the poetic word, so I translate it "judgements" (you know: scales like justice and trials like justice, a reference to the goddess Maat, perhaps... the scales of justice are ancient and probably ante-date Babel), rather than generic "calamities."
4 In 5, James is writing about burial clothes and the word I translated "garments" could mean "robes," or even burial clothes. It is not the same word as the "moth eaten clothing" from 2, which means clothing generally.
5 or "emphatic" on that verb, whether "ravenous" or "devouring" or "emphatic?"