I believe there are a few points to be noted here against Leighton Flowers view.
First, one could argue there is no difference in meaning between "know in former times" or "know of old" and "know in advance" or "get to know in advance." That is, if something about today is known in "former times" then it was also known "in advance." So one can argue that a semantic word game is being played, and all those translations say the same thing. It seems at some level Flowers understands this, as at 4:22-35 of the video he emphasizes that the meaning of proginosko is "simply to formerly know, to know before" (which is merely the timing of the knowledge, not anything about the content of the knowledge itself, which gets into the next point...).
Second, however, the way Flowers is attempting to view the word in that video, he does have a purpose for his making a distinction in phrasing (even if that phrasing does not really add any true distinction); he is arguing that the content of the knowledge is about past things at the time those things occurred (not content of things of today or the future at the time of the past knowledge). In other words, he is trying to make the "pro-" of proginosko be merely an additional emphasis on what a past tense ginosko by itself would have sufficed to say (or a past tense orizo). To illustrate, he is making an argument that effectively says the "pro-" prefixes could have been dropped from the verses in question.
Instead of what we have, by his argument, Rom 8:28ff could have simply read (using your translation given in the question, bold at the points of change):
"And we know that to those who love God, all things work together unto
good, to those who according to [His] purpose are called (kletos);
because them whom He knew (ginosko) He also ordained
(orizo) to be of like form with the image of His Son, so that He
[God's Son] would be firstborn among many brethren; and them whom He
[God] ordained, these He also called; and ..."
The "pro-" prefix in his view becomes superfluous, as a mere past tense verb without prefix would have sufficed to state the same thing.
Could this be the case? Yes—I see no purely grammatical reason to argue against the use of "pro-" in such away. But to me it seems highly unlikely in Romans 8 (especially, Romans 11, maybe) for three reasons:
- I fail to see any purpose in why God/Paul (DISCLAIMER: I believe in divine inspiration of the Scriptures, such that it is God's word as much as Paul's) would have a superfluous emphasis on past knowledge of past events being known and determined. In other words, there is no real "need" to have the "pro-" prefixed form of the verb used if that was the case.
Broader usage of these prefixed terms shows they are used as has been the standard interpretation, to know (ginosko) (or determine [orizo], but I won't give examples of that here) things prior to those things happening. Consider the examples given from a standard Greek lexicon: William Arndt, Frederick W. Danker, and Walter Bauer, A Greek-English Lexicon of the New Testament and Other Early Christian Literature (Chicago: University of Chicago Press, 2000), s.v. προγινώσκω. They cite passages like (bold added for translation of προγινώσκω; brackets are my comments):
[Philo of Alexandria]
Now the second species is that in which our mind, being moved simultaneously with the mind of the universe, has appeared to be hurried away by itself and to be under the influence of divine impulses, so as to be rendered capable of comprehending beforehand [προγινώσκειν], and knowing by anticipation [προλαμβάνειν] some of the events of the future [μελλόντων]. Now the first dream which is akin to the species which I have been describing, is that which appeared on the ladder which reached up to heaven, and which was of this kind. (Charles Duke Yonge, trans., with Philo of Alexandria, The Works of Philo: Complete and Unabridged [Peabody, MA: Hendrickson, 1995], "On Dreams" 1.2)
[Greek of passage]
δεύτερον δʼ εἶδος, ἐν ᾧ ὁ ἡμέτερος νοῦς τῷ τῶν ὅλων συγκινούμενος ἐξ ἑαυτοῦ κατέχεσθαί τε καὶ θεοφορεῖσθαι δοκεῖ, ὡς ἱκανὸς εἶναι προλαμβάνειν καὶ προγινώσκειν τι τῶν μελλόντων. ὄναρ δʼ ἐστὶ πρῶτον οἰκεῖον εἴδει τῷ σημαινομένῳ τὸ φανὲν ἐπὶ τῆς οὐρανοῦ κλίμακος τόδε· (Philo of Alexandria, “Philo, Volumes I-X: Greek Text,” The Loeb Classical Library [1934; Cambridge, MA: Harvard University Press, 2001], Vol. 5, "On Dreams" 1.2)
Notice Philo is explicit about stating knowledge content is of future things in the use of this word.
Accordingly he complied with what they desired, upon the promises they had made him, and was desirous to fall upon us when we were unprepared for him, and knew nothing of his coming beforehand [προγινώσκουσιν]: so he sent to me, and desired that I would give him leave to come and salute me. When I had given him that leave, which I did without the least knowledge of his treacherous intentions beforehand [προηπιστάμην (near synonym to προγινώσκουσιν, as the root ἐπίσταμαι means "understand," "know, be acquainted with")], he took his band of robbers, and made haste to come to me. (Flavius Josephus and William Whiston. The Works of Josephus: Complete and Unabridged [Peabody: Hendrickson, 1987], "The Life of Flavius Josephus," 106)
[Greek of passage]
ὁ δ ̓ ὑπακούσας αὐτῶν ταῖς ὑποσχέσεσιν ἠθέλησεν ἐπιπεσεῖν ἡμῖν ἀνετοίμοις καὶ μηδὲν προγινώσκουσιν. πέμψας γοῦν πρός με παρεκάλει λαβεῖν ἐξουσίαν ἀσπασόμενον ἀφικέσθαι. συγχωρήσαντος δέ μου, τῆς γὰρ ἐπιβουλῆς οὐδὲν προηπιστάμην, ἀναλαβὼν τὸ σύνταγμα τῶν λῃστῶν ἔσπευδεν ἐπ ̓ ἐμέ. (Flavius Josephus and Benedictus Niese, “Flavii Iosephi Opera Recognovit Benedictvs Niese ...” [Berolini: apvd Weidmannos, 1888–], Iosephi Vita, §106)
Notice Josephus is also referencing a "preknowledge" of someone's coming (in the negative, that is, it was not preknown), but the point is the content of the knowledge was about a future event.
So other contemporary usages of the term (i.e. historical context of the use of the term) seem to favor the fact that proginosko is used to refer to knowledge beforehand of content regarding a yet to be reality. This does not favor Flowers argument.
Contextually (and Flowers emphasized context in that video as important), in Romans 8:28-30, the "calling" is a pivot point. The focus is on "those who love God," which are also equated with "the called" (v.28). The point being made in this context is that the calling of any individual (v.30a) is stated to be based upon that individual being "preordained" to conformity to Christ's image (v.29b), which preordaining is based on a "preknowing" of the individual in some way (v.28b-29a).* And then the other items (justification and glorification, v.30b-c) are based upon that calling. This makes the "pro-" prefixes significant, because they come before the pivot point of the calling of those that love God, whereas the justification and glorification come after. So God knows and determines something about an individual before the calling, and in fact these things appear to be the basis for the calling. That everything is given in past tense (as Flowers emphasizes) means that, in God's mind, the whole is a package deal leading to and end result of glorification. But each step happens at different places in historical time.*
The above argument fits the more traditional views of Romans 8 better than Flowers's view (IMO).
The Romans 11:2, as well, implies in context that the present subject (Paul himself) and additional people who "at this present time" (v.5) are "a remnant," were preknown by God. That is, I do not think the "pro-" there is merely a reference to knowledge of people in the past, but also those of the present context that Paul is referring to. (However, in the context of Romans 11, I do think there is more contextual argument that at least makes Flowers's view equally plausible as to the content of the knowledge being referred to).
Even Acts 26:5, I believe, can be argued as a "pre-knowledge" idea. Not in the sense of the Jews prophetically knowing Paul, but rather that they knew Paul from the first of his youth (v.4), and they knew prior to his actually living out his life "according to the strictest sect of our religion ... a Pharisee" (NKJV) that the Pharisaical path was the course his life was going to take. An analogous idea might be a child who shows at a young age an evidence of what future career they might pick.
I do not find much support that the content of what is known when proginosko is used refers to something previous (i.e. as merely an emphasized synonym for a past tense ginosko), but rather to some content about reality that is yet to come at the timing of the knowledge. (FYI, I like some of the information Flowers puts out, but on this point, I don't think he has a correct grasp of what this word is intending in these contexts.)
* The two points above I have asterisked relate to getting theological: My personal view on the Romans 8 passage is that God preknows who will come to "love Him" (v.28, which love is evoked because of His first loving them, 1 Jn 4:19, which love in part entails His love for the whole world, Jn 3:16). Those that will love Him, he has predestined to make new (conformed to Christ's image), and will call them (to belief in God's saving work in the Savior, Jesus Christ) for the purpose of His being righteous to justify them (despite their sinfulness) and then glorify them. This, of course, is only tangentially related to your question.