BTN has overall vpip/pfr: 17/13 in 9max plus 3bet 8, cbet 71 at 1057 hands.
I think preflop villain would open around 45-50% of total hands.

So my assumption on how villain plays the flop is as follows(I am a beginner player):
I think he checks behind all live cards with no bdfd(he bets all or most of the combos of live cards with bdfd) except of some exceptions with bdsd potential(like 87o, although I am not sure how he plays those). He also checks behind all kings and A8-A2(84 combos). Also all 9s with no fd. Also QQ, JJ, TT, 88-22. So he would probably bet, at least most of the time the gutshots here of QJ, QT, JT. He would also bet all 2pairs, sets, top pairs of AQ, AJ, AT. He also bets all of his flush draws(at least most of the time).

Now here since most of the time he probably bets his fds on the flop, we don't have to be concerned with him having a flush often. This turn card gives him a set(88), 2pair of 98, K8, A8. All those are a lot of combos in comparison with the total combos of his range. Villain has also many top pairs which call. And I guess his kings fold here. I think betting with our King here isn't good. But If he calls his fds here(a lot of pocket pairs get a fd plus many more combos) then we might want to bet in order to not allow those hands to realize without paying their equity.

I think folding might be better here. If he checks JT on the flop then he might show up with that here. If he is not bluffing often then I guess fold is better.