I think he never has the nutflush or K-high flush on turn because 99% of the time he would just pot turn with those hands.. why else is he calling your flop re-pot if not to get it in when he hits? So, he either has a low set or 2pair or some good wrap maybe with a lower FD like J
9
xx or like apir+FD with the T
, and decided not to get it in for 200BB, but to see a turn and re-evaluate.
That said, I think you have the best hand probably 95% of the time on turn, and if you think he would spazz call with a set or lower flush, then pot turn. If you think he may choose to bluff river, or he may be more inclined to c/c river with sets or loser flushes because you check back the turn, and he doesn't think you would do that with a flush - then check back turn and call river if he pots or pot yourself if he checks. However, 20% of the time the board will pair on the river, and if he pots then, you might have to fold...