You have more than a flush draw, because you have overcards to the board as well.

I don't know what those PT stats mean, but you make it sound like Villain could have a pretty wide range of hands here. If that's a case, you're a solid favorite against his range. I would lead for about half the pot and see how others respond. Note that this bet does not give straight draws the right odds to play, since some of their outs are dirty.

Is Villain the sort to raise a draw here? If so, you can come back over the top of him and try to take it down now. If you think a raise is more likely to signify him trying to take control of the betting from you, I'd just call and see the turn. If it pairs you, I think you need to lead out again, so that he can't take a free card. If you make your flush, check to him and let him try to represent your hand or take a free card and hopefully catch up a little. If you miss, I'd check and either check-raise all-in or be happy if he gives me a free card.