oop I will probably either check raise all in or just check fold depending on reads.
As played I probably shove though,
He 3bet after a raise & caller - slightly more likely to be squeezey
A min raise gives great drawing odds to a flush & is not a standard line for someone who 3bet AA/KK to the to the right amount pre-flop.
Its still very close though.

- I dont like check call so much oop in a 3bet pot as you're going to to check to him on two more streets and it seems it will be to easy to move you off what could be the best hand. (Most people wont slowplay a set, AA/KK in a 3bet pot on drawy board so by the time you get to river your hand will be face up.)