Um If you're in the BB how do you raise to get a free card on the turn? This makes no sense.

No it doesnt make sense. You can't get a free card when you are first to act.

If you got in this awkward position, after he 3 bets you call. Check call the turn and check fold the river if you dont hit your flush or backdoor straight.

Straightforward. Check-call the flop
check-call a missed turn, but out if you make it.
check-fold a missed river, bet out if you made it.

The reason you don't go for a check-raise on the turn like everyone else does, is it gives your hand away. The stop and go makes it look like you are stealing and you are likely to gain extra bets if he raises.

Just call his bet on the flop.

I would bet the turn if you hit your flush, but it kind of depends on what you know about the player. Check/raising might be the best move actually, now that I think about it. Then, bet the river.

If you don't hit you flush on the turn, I might just fold since you haven't lost that much on the hand. But it depends on if you hit a card that gives you a straight draw. Then, I would call his turn bet.

EDIT: Check/raising the turn might be advantageous, because he is likely to call the raise. You will get a little more out of him. On the river, you bet again, and if he folds, it's all right. But he will probably call again. I don't know if it would give his hand away, because you have know idea what these guys play. He might have two pair, and will call any raise. Or, he could be the guy who can't let go of TPTK.