I recommend you watch the video then, because the question was asked TO CALVINISTS in a recorded Q&A, and Dr. Flowers replays their own words.
My first comment is that he has Judas clearly wrong. Jesus chose Judas knowing exactly who he was - knowing exactly what he was going to do. Without that, the plan of God would not have been accomplished.
Jesus answered them, Have not I chosen you twelve, and one of you is a devil?
John 6:70
This plan of Redemption goes back to Genesis (and beyond) so it wasn't like God decided to choose a time when he might find the man He was looking for. God - who works all things after the counsel of His own will - foreknew each of the 12 (and knew that Judas was a "chosen devil"). Otherwise, God becomes a victim of circumstance who has to plan His way around man's choices. So I think Flowers is dead wrong on Judas.
And I also think it links in to his presupposition that God has to be a certain way to every man equally and every man has to have the same opportunity presented him. He essentially has to say that the theologians on the stage are judging God's grace but he has to judge people's hearts by alleging everyone has the same opportunity to be saved. Because at that point, their salvation hinges upon their choice and Flowers has to believe (therefore) that a man who is not saved is not saved because he decided against God in some rational process. He has to judge the heart and mind of the hearer. Nowhere (that I read) is this said - that all men everywhere have an equal opportunity to be saved and have the same grace given to them unto salvation. Psalm 145:8-9, again, is not about salvation. It is about the goodness of God to all His creation. The rain falls on the just and the unjust. But it doesn't imply that God owes every man a certain measure of salvific grace. So when reading Titus 2:11, he has to choose a translation that specifically says salvation is brought to all people (I won't argue the definition of "all" here since I don't have the Greek background, but there's nothing that I know of that requires it to say every individual without exception - otherwise, I repeat that we all need to be universalists). Remember that Paul also said that the Jews read Moses with a vail over their hearts. Christ appeared to them but they were restrained from "seeing" the truth. It appeared to them, but it didn't benefit them.
I won't revisit God's drawing (as Flowers quotes it) since I think I did so in my first response.
The point about David praying to God about whether or not Saul will kill him - I don't quite know where he is paraphrasing from, but he doesn't give any citation. Even so, he's pushing an idea that God doesn't necessarily know what the outcome of things will be - He only knows contingencies. That's the only reason I can see Flowers including this because it really doesn't have any impact on the original topic. And all God was saying was if you do X, Y will result. Just like He told the Ninevites by Jonah (who had the free choice to reject God's call, right?) that he was going to destroy them. Even Jonah sat and waited for it. But it didn't happen (not then) because they repented. God even said through Jeremiah that any people that repented would not face the judgment He promised them. And the generation of Ninevites that repented were saved from that. In the end, God still destroyed them - just gave the ones that repented a reprieve. So both happened - He repented of the evil He was going to do to them and He also eventually actually carried out the evil He promised. So it's really very simple. God knows. Otherwise, Moses should be credited with calming God down and preventing Him from wiping out Israel entirely and starting over.
This may be taking it a step away from the thread, but my personal view is that the offer is - in some sense - universal. But just because the truth is provided doesn't mean the individual will hear or accept it. And this is where one has to either decide to judge someone's heart (which I believe Flowers is doing by saying unbelievers freely and knowingly rejected the gospel) or recognize that there is something more than just objective truth needed for someone to bring someone to true faith. The Calvinists have it right in that we don't know who is saved and who isn't. That IS in the hands of the Lord. And while it may be a bridge too far to say God has to determine who will and who won't receive a certain kind of grace and/or a certain kind of mercy in order to be saved, it is absolutely true that :
...He saith to Moses, I will have mercy on whom I will have mercy, and I will have compassion on whom I will have compassion.
So then it is not of him that willeth, nor of him that runneth, but of God that sheweth mercy.
Romans 9:15-16
Anyone who thinks it unfair that God gets to decide who He shows mercy and grace to is just as bitter (though in a different way) as the Calvinist who is one of the "frozen chosen". That's why it is such an Amazing thing when God does show Grace - and the heart that seeks after that - seeks the Hand of God because he sees the goodness of God in the lives of men who have know the richness of His grace -- those are the men who have been granted some degree of grace to pursue Him in the light of the work He has done in select other men. The Apostle Paul was one of those men, but there have been others. John Newton seems to be the natural choice for that. He knows the Grace God lavished upon him and he was a Calvinist. And while he couldn't see any other way of viewing God's grace properly and biblically except through a Calvinistic lens, he was not so dogmatic as to enforce it on others. His letters show this clearly. I believe that much of what passes for Calvinism today is tinged because it tends to attract those who are more educated - and so it is quite likely that many such professors are really unregenerate. And truth in the hands of the unregenerate can be very ugly. Calvinism naturally tends to emphasize God's glory while Arminianism focuses a whole lot more on man. So it tends also to be more palatable (regardless of who promotes it). That's just my own observation.