Axs with a flush draw and an over-card is about a coin flip vs a pair. AKs with 2 overcards and a flush draw against pair is a favorite.

With a healthy pot, you should push hard for fold equity unless the money is really really deep.

In a smaller pot, you might be better off just drawing because there isn't much to steal.

With shallow money it's an easy push.

With deep money, these spots make my head hurt. Your biggest threat is missing the turn and getting pushed off your hand. Try to raise the flop to check behind on the turn with position to prevent this from happening.

If the board is paired, you need to be careful, probably one of those NL spots where you might just have to let it go to heavy resistance.