Not without some serious reads, but you could size up 4-bet and just 6- bet AI.
Dont worry about running into AA here there will be 6 combo's of better hands in most villains range's from BTN here. You have just happened to run into one.

Did you make screen name to post bad beats? :D (truth plz)

It's not a super cool spot to be in honestly, but I don't think we can fold kings here. I would just get it in preflop, once he makes it 12 dollars I would just rip it in, because we should not have fold equity, and if we're not folding KK, we might aswell get the money in.

Nothing you can do.

For some time I thought it was possible to get away from these coolers of KK vs AA with some hero folds preflop but then I started to see people doing weird and big mistakes so I never fold KK pre. I would play exactly the same way