This is a discussion on KK against Ace on flop within the online poker forums, in the Learning Poker section; I'm struggling a lot if I have KK and on the flop shows up Ace with some other low cards like offsuit.
In most cases
KK on A high flop is not a 3-street hand, and even less so in a multiway pot. It also does not need a lot of protection, since nobody can make a better 1 pair hand, unless they have it already. So where for instance it often makes sense to bet 99 on A83 to deny equity from random overcards, with KK the best play is often to check back to catch some bluffs or go for light value on later streets. The key is to control the size of the pot and avoid entitlement tilt. You had the second best hand preflop, but now its only a medium strong hand and must be played as such.
With two callers and being out of position, I would mostly CBet the flop as yoor range would have most of the aces. If I get a caller on a dry board, I would probably give up my hand and not put any more money in the pot. If you have a more dynamic flop with draws and such, then these draws are more to fit into the the other players ranges and I would invest a little more money in my hand, but depends on my opponents reads. Would definitely not put my entire stack in against two others post flop. This hand has maybe two streets of value unimproved
Yes this is always a scary spot. If you really think you are weak postflop, you could consider putting going all in more with kings once you are 3-betted. That would be the easiest way to fix any leak.