without reading any of yaawns post before writing mine in this spot I would recommend checking back the flop because betting puts you in a spot where if raised you are basically screwed vs the guys range and there isn't much value in betting but if you check u give urself free cards to hit flush or set with your kings and once u get that u can prolly get 2 streets of value from hands that outflopped u but then end up being behind

checking also sorta balances ur check back range a bit because its a hand u can probably peel at least a turn with so ur check range isn't just total whiffs that u wanna give up entirely.