Rough estimate calculations: he throws in ~1/3 of the pot for a 1/6 chance of hitting his flush on the turn.. not a great idea by him, but implied odds are there too, as can be seen here. After his flush hit, he

If we calculate it for turn+river, he has made a 'break-even' bet here.

It is complicated to know which interpretation to take, as there'll be a probable turn-raise if a flush does not fall, which adds to the cost.. and there are 'implied odds' which add to the benefits and both are kinda uncertain.

Sry, not really advice, just trying to do the math. I probably woulda done the same here.. don't think you could readily he was going for a flush draw. Personally I woulda checked on the river.. since there is now a flush AND an overpair possibility out. But that's just me, dunno what is "best"