ugh this is a really disgusting jam unless you have a read that villain is a whale... What do you mean from a GTO point? Doesn't that imply that the EV will be 0EV for both players?
To calculate if the river jam is + or - EV...
%heFolds * pot|heFolds + %heCalls * ((finalPot * equity) - investment)
If you just want to know what your required FE should be in order to at least break even with your jam, then:
investment / (pot + investment). in this case...
1345 / (240 + 1345) = 0.8485
So you need ~85% FE in order to break even on the jam. If you think he folds more than this then shoving ATC becomes profitable.
We don't care how often people generally hit flushes, the fact is that we are on the river, there was a FD on the flop, and villain is now on the river with some range. We only care about what % of his range has the flush, not how often ppl hit flushes from holding 2 suited cards (is that what you meant in your OP?)
You should take that preflop opening range now and shave off hands that don't play that particular way on each street. Once you get to the river, split his range into 2 based on (1) combos that call a jam, and (2) combos that fold. To get the % combos that call, (combosCall / totalCombos). Then your FE = 1 - %calls. Then use this information in the above EV calculation to figure out if your jam is +EV or not.