Generally you want to bet at least 3 times the original raise when you 3-bet to not give mediocre hands the odds to call, so raise to 3.6 pf or just call/fold, his raise screams of KK/AA. His check-raise on the flop is not huge, he raises from 3 to 12.69 while a normal raise would be about 9, so he's all-in either way. You beat nothing but a bluff, easy fold.
These are the kinds of flops where I would consider not cbetting at all and just letting the hand go when I whiff w/ AK. Heavily coordinated boards w/ a flush draw are very tough to play OOP.
And calling the push...well...that's just..uh.......no.
Ur three bet is way to small pf... Don't mind your c-bet here, don't think its a terrible board, but just fold when getting raised, ur hand is air... It's a call bluff