4pot KK dry board

Contrary to what many people think, flating KK preflop in this spot is totally fine. I'd even say it is better than 5bet.
I would shove the turn as played.
Anyway you have to call the river bet as well. Don't be afraid of flushes.

This guy has AA almost always, you can fold PF, or you can call for a set, you have the right odds I think.

If you think he's only 4betting with AA I would fold for sure pre-flop with only $4,02 effective behind if you would call here. You don't get the implied odds to call for set value only. Post-flop seems fine, but most of the time I would shove the turn when he's checking to you.

Cheers,
SDK1987

No it's my mistake. I thought that the original raiser on UTG is 4-betting, but it's another player, so well played in this case.

You don't get the implied odds to call for set value only.

Why not. Provided that he'll call 100% of the time we have .15+.52+1.2=1.87+4.02 (his remaining stack) =5.89 and we have to call .68 to win 6.57 so about 1 in 10 and we will hit a set 1 in 8, so it's +EV, not much though, because we'll lose sometimes when we hit and if we take the rake into account it's about BE probably.

I think a call pre is fine with KK especially against what looks like to be a nit however one thing I would like to add is why don't you use 4b range instead of total 4b (just a suggestion) as you have a decent sample this will give you a more accurate reading than total 4b. As played I think you played the hand well maybe take a note that villain checks turn with AA in 4b pot with intentions of check defending?.