Based on your description of the villan I am putting him on a big hand, AA, KK, QQ, JJ, TT, AK, AQ....

Flop - So on the flop you are behind AQ, KK, JJ, or TT. Considering you have the a K and a J, I would decrease his possible holdings of KK or JJ. That leaves us with AA, QQ, TT, AK, and AQ. I think that it is safe to say that he is betting the flop with any of those with the possible holdings.

So lets say you have 4 outs to a FH, and 4 outs to the nut straight, and 1.25 outs for the BD flush. that is 9.25 outs to improve on your already very good 2 pair, I think that I am capping the flop. This will also give some strenght reading moving forward.

Turn - if he opens the turn after you cap, then I would slow down, unless you hit one of your outs, then I would pour on the gas. As you played it, I think that I would raise and then 3-bet, then if he caps again slow down on the river.

River - If you hit an out, hit the gas (although a 4 to a flush does you no good here, so you were down to 8 outs). Otherwise based on your read and other action on the hand I call down, which is what you did.

Margon <-- really bad, so advice is likely stinky.