I don't understand your question quite well.
There is no flush which beats your Hand. I would say easy shove?! Sure villan can have quads and maybe some weird K3 Combos but I would say you will win this spot on NL2 nearly every time.

I have problems in this spot too. I don't know what the answer is. But given the bet size, I would call, expecting to be beat a lot. You only need to be good 25% of the time.

Keep in mind that if you check river here, you have to call sometimes, otherwise you're very easy to play against. If you're folding 33, you're folding everything except a King. Flushes make bad bluff-catchers because you want him to have a flush, and you also lose to a random 2. So you need to check some of your Kings on the turn or river. The other day, I had a hand with a super aggro player where I check/called with my King on the turn. On the river, the board double-paired and he got stacked with a lower boat.

In general, I would bet bigger on the turn. He has a lot of Kings and flushes in his range. Both will pay off a bigger bet. He might even raise you with a flush.

can try and block bet river. This hand benefits from it a lot, and It is not like you have a ton of value with Kx(mean you aren't called by worse often).

Would bet larger on the turn for sure and river isnt great but prefer block bet/fold as he's never folding a flush and will probably only raise Kx. Not too many random air floats either on the turn that will bluff raise as most of them are likely A high that will mostly call or fold.

This hand has a very trivial xf otr in my opinion.
Block-betting for around 1/4 pot is probably ok as well.