AQs - calling 3bet pre-flop - calling flop and turn cbet with nut flush draw?

nice hand. absolute standard.

regarding the loss:

you had a lot of equity in the hand, but you did not get there. villain has tripple barreled.

so there were multiple things, that could have gone in your favour, but didnt.

you can not win every hand.

Pre is totally fine.
Flop is also fine.
Turn is a bit more close. Because the board paired you have some reverse implied odds, but I think calling the turn is not terrible.
River is a fold.

(Think only really TTs are in his range, 77 seems a little loose).

You are correct. I think even TT would be a little loose, but that totally depends on how villain constructs his 3betting range. Snowie would use more merged approach and 3bet TT but for example I like to do it more polarized and 76s would be in my range.

I lost a fair amount of money on this hand - did I play it wrong anywhere, or was that the gamble and sometimes I will be paid off when my flush comes in?

The thing with playing draws is that you don't hit very often, but when you do it is a big payday for you. We can use a simple pot odds calculation to figure out how often we really have to win this in order to break even. The answer would be ~29%. As I said earlier, calling turn is close but with some implied odds I think it is fine. When you call there you should expect to lose this hand often since you only hit about 20% but still on the long run it will pay off

Folding OTF has (imho) higher longterm EV. If u r calling OTF you should do so against a villain who is capable of folding OTT to a raise. And for this you need 1) particular villain with 2) big sample.

As played well played the river.

Thanks for the in depth analysis guys. Lots to think about.