I use to 3bet AK routinely, but according to Janda and Pokersnowie it's definitely a flat sometimes. The hand actually has pretty good implied odds and by flatting you can keep weaker aces and kings in. I'll pretty routinely 3bet AKs, but facing an EP raising and no callers yet I'd definitely consider a flat versus certain players.
Also against larger sizings I'm more apt to flat.
If you're looking for more bluff 3bet combos you can throw in A4s and A5s, that's what pokersnowie does.
There's a hand where Hunter Cichy flats AK in the BB versus a larger sizing which I think is a pretty good example of when to flat with AK.
https://www.youtube.com/watch?v=2kzodHn9aIM&t=456s
First hand^.