I would play it the similarly a majority of the time(would need more reads on villain to make a more concrete statement).  There are a couple things I want to bring to your attention to help in future spots though.

First with a nut flush draw you can never be drawing dead. In fact you are pretty much never worse than 25% in a HU pot(In this case not really worse than 28%).  However in this spot, where its a 3 flush board, and an A, you are also RARELY ahead.  Ocassionally you might see someone show up with Qhx, but not that often. 

If he would have shoved over your c bet, this is probably a fold.  A lot of the value in flush draws, especially nut flush draws when you are never dead, is fold equity, and value versus worse flushes.  In this spot once he raises you, you can rule out a lot of his worse bare flush draws, in the sense that he likely has at elast a pair with all flush draws. 

Lets examine the Fold Equity in this spot.  Well first thing we can look at his position, BB, which means we expect a pretty wide range.  He could have a wide array of hands, including a lot of flushes, and two pair type hands.  How many hands are raising us though?  He could feasibly raise AxJh/AxTh type hands, he probably raises all flopped flushes(or at least raises it most of the time), and almost always raises his two pair type hands. 

Then there are times he will raise as a semi bluff or even pure bluff.  This will happen somewhat frequently on monotone boards.  This is because its dangerous for the person facing the raise to call down light, because your not getting hands liek what you have to fold, and even if you may be ahead, the board can easily get worse.  So when he raises we expect you to reraise or fold majority of the time(there are def hands you can/should call though!).

Its really hard to know how often this happens without more info on villain though.

Value from lower flushes in this hand probably isnt that great though.  The only time this happens is when he has the Qh and occasionally the Jh, but the problem is we are winning a stack when we hit, but how much does it cost us when we miss?  We also have to think about the heart COSTING us money against all his non flush hands.  If we call here.  We hit turn about 20% of the time, and miss the other 80%.  However of the 20% we do hit, how often does he have a hand that pays us off? And of the 80% of the time we miss how often can we afford to call another barrell?  Will he ever continue bluffing in this spot?

These are some things you need to think about.

In the end, I dont mind your play readless, I think this is a spot where we cant really call.  We have no gin cards outside of hearts, which probably cost(in the sense of killing action) us money more than win us money.  Sure a J or K may be a good card for us, but it could also just spell out more trouble, and we can no longer get any hands that we beat to fold considering SPR after a turn bet from villain is just too low.

HOWEVER! I do not liek your shove, I much prefer to just make it liek 4.7-5k and shove the turn if he makes the horrible msitake of calling.  I would make this size raise with the top and the bottom of my gii range in this spot.  AKA my good flushes and my hands like this.  So in the end I like raising here, to maxmize FE and add balance to the top of my range.

Getting in the nut flush draw on the flop is usually not a mistake.