.3/.6 NLH
UTG limps

Hijack (Hero $55) raised to $2.40 with 6s6c

BB (Villain $100) calls

UTG calls

Flop Kd 6h 3h Pot= $7.50

UTG checks, Hero (HJ) bets $3, Villain (BB) calls, UTG folds

Turn 4c Pot = $13.50

Villain checks, Hero bets $9.90, Villain calls

River Th Pot = $40

Villain shoves for hero's remaining $33.

Hero should? Can I just give him credit for a flush or is it to tight to fold a set? Thanks!

In this case the BB call range is relatively wide. This also depends on the rate of hero increase. Which in this case was a standard size, taking into account that the V2 limp from UTG. On the flop the cbet was a good size, keeping in mind that you should protect your hand and charge a higher price to the draws that at this moment will want to continue.
On the turn the fairway is a brick that does not interfere too much with the ranges involved. I think that on the turn the second barrel is also correct. Considering the texture of the board, we can't easily deliver a cheap river to the villain. And finally on the river the flush line is completed and V's donk bet is very indicative of value in this case. I think it's a good fold, since your range doesn't have enough capacity to catch bluffs here. In addition the villain eliminates with his bet many bluff combos that should be protected and basically with his leadership he is showing the strongest part of his range. Possibly fold is the most standard option here and I think it would in this sequence as well.
Greetings.

Preflop
Standard isolation spot.

Flop
When there is a limper in the pot, there is also at least one fish in the pot, and then I dont like this modern GTO style downbetting, when you essentially flop the nuts on a wet board. He wants to pay you off, so just bet large here, print some more value, and cut down on the implied odds of those draws, that are available.

Turn
Some gutshot draws got there but still a clear value betting spot. I like the large sizing.

River
Actually pot was 33$ with 40$ left behind and not the other way around, so you were facing an overbet. Even so if you want to play GTO poker, this is almost certainly still a call. Your MDF is around 40-45%, and this is almost certainly in the top 40-45% of your range. You dont block the flush or straight, but its more important, that he could from time to time be doing this with a worse set or two pair like KT.

However from an exploitative standpoint I think, you can perhaps fold here, since he can have a lot of flush combos with only low flush cards on the board, and only a few busted draws are available. So it seem like a spot, where he is most likely skewed towards a flush and not bluffing often enough.

Hero - fold in the river - villain had flush for sure, I think
hero's remaining is $39.7 not $33! where you lost $6.7? no makes sense
open 66 like that ( $2.40) is -EV in the long run, I don't recommend
because you have less than 10% chance to hit a set in the flop, and a weak pos-flop playability...
and that is a full ring cash... if that is 6max is ok