wouldn't the $$ I needed to make be $0.08 after I called on the flop?
I'm honestly not sure without doing the algebra. I thought about this a bunch of ways and all of them seem pretty logical. Just gotta break out the math and see what it says.

Either way, I don't think it's a huge deal. Even if you do need to get $0.08 into the pot, as we see in this hand, that's a 1/4 PSB OTT. I'm guessing that tiny bet isn't really on your mind when you catch the flush OTT.

Even if we call another 1/2 PSB OTT, and we use your suggestion for the needed equity to make that call, then we're now in for $0.08 + $0.16 = $0.24, which is still less than 1/2 PSB OTR, so within the expectation of a call from many Villains.

Should we be assuming one of the villains behind us will make the $0.08 call so that we can calculate the size of the pot and future bet we will be facing on the turn if villain decides to barrel again? Kind of difficult to know if anyone behind us will call so maybe not
Same as always. You put them on a range now, and you speculate as to what % of that range calls and what % raises and what % folds, then you do an equity calc that includes the EV from that villain's response. Do this for each villain left to act after you. Use Equilab to calculate equities, and multiply those frequencies by their equity of the pot and add them up for your total EV.

It's much more complicated when it's not HU, so I kinda don't recommend diving in that deep until you're much more snappy and quick with the HU situations.