well i think betting something like 121 or shoving both is fine. Shoving cause it looks bluffy after he check called turn.
But to make him call that river he'll must have a jack or a made flush. imho villain will like never have a jack there. I dont see a lot of people bet calling a huge raise on such a flop with a jack, well maybe QdJx but that's about it.
A slow played made flush on 3 streets is unlikely imo, he should at some point take the initiative. So imho he's gonna have more often a king there or smth where we'll get no value from anyways like a fd.
imo the jack on the river is bad because he's gonna call less with a king there.
in a game theory point of view you should never bet less when u want a call and bet more when you want a fold... but against an unkown who never ever can exploit you anyways it might be an idea to bet less, to get a call from a hand which is more likely in his range than those he'll fold to a big bet. I've asked myself once arrived at river... what betsize would i call with a medium king?