Im not sure about the flop call, you do have a lot of BD potential and that is a weak bet for a drawy flop.
The turn, when he checks here I think you should check back.
If he has a weak hand (something you can fold out) then you have almost 40% equity against that hand.
Now when you check the turn, he will check some % of rivers and I think you can throw out a 1/2 pot sized bet and win many of the times he checks the river.
So overall, I think you have the best hand if you check the turn.
The other great thing about checking here is if he then thinks you have given up, he is likely to bluff a high % of the time on the cards that make your hand on the river.
An ace, a king a ten another flush card, all great bluffing
cards that make your hand.
The problem I see with betting is this flop hits his range and when he folds, he mainly folds hands you beat and when he calls, its always with hands that beat you but will less inclined to call a river bet should you hit your hand.