This is a new discovery for me, so I thought I'd share it (also had a few hands like this last night).

Where AA with flush draw is in trouble for serious money is against top set. So, let's say you have some kind of MP raise sitting on your AA with nut flush draw, and the board comes K94ss with your flush. Here's my opinion: If someone other than the raiser bets, they almost definitely have KK here, and you're 2.2:1 against that hand even if KK has no blockers or anything. So, you don't want to play for stack.

BUT... AA with flush draw is a pure coinflip 1.0:1 (49.76% equity for AA, so negligible underdog) vs. naked top 2 (no real draw), which becomes a lot more likely on a board like KJ4, although you're also going to run into KK or JJ (from which you may have fold equity) some of the time.

Where AA with flush draw does really well is against even monster draws. In those cases, it's pretty much always favorite (not huge, but still sometimes sizeable).

Examples: You have AA72 with hearts to one of your aces. Board is Th9h4s. You're now a 1.5:1 favorite over KQJT with one heart, and you're a 1.3:1 favorite over KQJ8 with its own heart draw (no pair, but biggest possible straight draw).

I suppose I should also have run JT98 with heart draw on that board. I think you'll be underdog, but I doubt less than 60-40.

My conclusion: In situations where you strongly suspect that you're up against some kind of wrap rather than a set, you should go ahead and try to push your AA here. If the board looks more like you're getting involved with top set, then it's better just to go away. While it could be worse vs. top set (against middle set, you often have fold equity), it's really not worth playing for stack, and you don't have odds to call to see the next card (unless they'll try to fill up on the river and still call pot if you make it on the turn).