[Proofrock]

You're about 2 to 1 against making your flush by the river, and you can count your ace as a partial out. you have t360k and the pot is ~t140k. Pot odds dictate you can't fold to a c-r if you bet anything more than ~1/2 pot. Since I can't fold to any reasonable c-r, I like betting the flop between t90k and t120k, with 100k being my first choice.

If Villain c-r, you get all-in on the flop.
If Villain c-calls, checks the turn you have a choice:
-take a free card if you miss
-push if you miss
-check behind if you hit (representing a missed CB)
-bet whatever you think will get the money in the middle if you hit

My personal favorite of these choices is to push the turn if you miss. Firing on two streets against one of the few players who can break you would make me read you for a very big hand, and I expect you have a lot of FE. Of course, for that very reason pushing the turn may be stupid.

If Villain check-calls flop, leads the turn, then I'd let pot odds make the decision for me.

I really hate pushing here, if for no other reason than it looks like missed overs/a draw. I rarely see AA-88 push here.