Stack off. I think shoving is correct. If he's drawing then you've got him good.

I doubt he has AA since he flat called your 3-bet PF with someone else left to act.

After he flats your flop bet I think you can narrow his range down a bit. I would say QQ-TT,66,AhKh,AhQh,AhJh,AhTh,Ah9h,Ah8h,Ah7h,Ah6h,Ah5h ,Ah4h,Ah3h,Ah2h,KhQh,7h6h,6h5h. You may be able to discount AKs & KQs since you're holding blockers. Against this range you have 46% equity.

If he has AA or a set and didn't raise the flop, oh well. Get em next time!