It was a bad call because you pay 2 times the value of the pot to see your flush. That's mean that we have to win 40% of the time when we are calling that size of bet. While we had only 32% to get or flush. So, you had to fold.
After the shove there is 1200 in the pot and Hero needs to call 780 to win it. It is true Hero needs to win ~40% of the time to break even and there a 9 flush outs twice. the rule of 2 and 4 (multiple outs by 4 for odds to hit with 2 cards to come)
tells us the ods are ~36%to hit (true odds are 9/47 + 9/46 =38.7%. The alone math justifies the call As played Hero was the favorite given hero's 2 over cards to the pair add 6 outs. The same if Villain held A2 or A3..
One needs to look at Villain's range. By calling the flop, her range is capped, given she'd likely raise big pairs and AK. She definitely has 77 in her range, but does she have 22 or 33? She also has TT, 99, 88, if she has 77. he also has A7, A3s, A4s and K7s and other other flush draws. Against trips Hero has the flush outs, Against A(7, 3 or 2), K7s, 87s, and 76s Hero is ahead. He is losing to the bigger flush draws but there is only one combo of each call it 10: AJ, AT, A9, A8, A7, A6, A5, KQ, KJ, QJ,
When I plug all of that into my PkrCrusher
App, Hero is just a slight dog. Given that Hero had just under 20 BBs in his stack, the only question I see is whether he should have folded or shoved preflop instead of raising. My Float the Turn app says its a shove preflop, but its border line.
As played, once Hero puts 11% of his stack in preflop, he needs to be thinking about shoving himself if he hits any piece of the flop.