I stick em all in his eye here (although I dont play at this level).
He could easily have Adkx and do this. If he has a made flush then it will be a small one (maybe an open ended str8 flush?)
You have plenty outs both with 2nd nut flush if he has a small made flush and the house as well.
You could well even be ahead in this spot already. He has plenty fold equity here with a semi made hand!
can rule out AdKx as he didnt 3 bet pre
From stats he is a clown, so the check minraise is usually a huge hand.
I would call and fold river if i dont improve