You would not betting the flop per se, you'd be attacking his apparent weakness. If he reraises you can easily fold and note that he's probably minbetting good hands to induce bluff. You could do this with any two, but in this hands you have the added bonus of possibly having the best hand right now, you have your two outs that are probably good, and you have some backdoor draw possibilities as well.

As played, I'll bet out the turn and call his push.

Remember to note that he minbets his draws in position instead of taking a free card.

Oh, and don't go AI if you worry about someone being on a flush draw. You want him to call incorrectly if he is, so bet out the largest amount you think he would call.