3 limps H sees K3o in BB

flop k38hh
H bets 15... fishy V calls

turn k
H bets 20... V calls

river 9h
H checks... V checks back with K7o

Put V on fd since there is only one more king out there .. flame away

3/5 game? Stack sizes?

Flop is ok, bet more on turn, about 45 is good.

You think villain had a flush draw, and now the flush draw got there, u should continue betting to get paid off? So why check??

it's 1/3...300ish effective

bet turn small to keep FDs in ... coz there's only one K left

river was FPS trying to c/r since this V doesn't like to fold

Fishy Vs don't fold to bigger bets when they want to draw to the flush. Bet the river for value, especially if you think he was drawing and hit on the river.

I don't believe going for a c/r on the river was the right play, even if you would find your V to have the flush 75% of the time. He is not always going to have the nut flush & by you checking, you allow him to set the size of the river bet.
So, he bets $X [the value he puts on his 76s flush] & you c/r to $2X.
He folds because if you don't have a better flush, there is also the pair on board, the fact you led the whole way & now are showing real strength with a c/r on the river.

By betting out, you give away less info about the strength of your hand, giving your opponent the opportunity to raise with his nut flush.

Finally, if the player is incapable of folding a weak hand [K weak kicker] you get paid off on the river instead of hearing him echo your "check"

So, stop doing. That is, IMHO.

P.S. That's a damn dry board on the turn for those without a set, K or flush draw, so I don't see anything wrong with your turn bet sizing.