Turn you should probably be mixing with your flush draws, this turn is essentially a brick as villain has very little if any 4x here so we want to go quite big and polar with a value range of KQ+ so we're not going to have loads of bluffs. Also in these spots it is possible that villain shoves on us if we barrel so we really don't want to get shoved off our equity by a strong player that realises they can deny equity in this spot as folding a flush draw here sucks. I think we want to block KQo so having the Qh would be a nice card to have. After that I think we should bet with our lower flush draws first because our villain is likely to shove flushdraws as a bluff and we don't mind folding these hands as much because we may have been dominated and lost the pot anyway if we decide not to fire the third barrel. Be really careful with betting combo draws here because they have a lot of equity but may not quite have the equity to call a shove, I think with this SPR you should be fine if you use a large enough sizing but as you get deeper this is something to be really careful of, folding 8h7h here is a disaster.

With your specific combo I think both bet and check are probably fine, I would probably lean towards check because if we hit a jack on the river a lot of the time we're going to be good when checked to but if we bet here our second pair will very rarely win the pot at showdown unless we're specifically facing a missed flush draw. Having said that villain is more like to have AhJh or AhTh than weaker nut flushes and blocking the nut flush is quite nice because villain will call 2 with that hand and we'd really like folds now so honestly I think you can go either way. If villain is not the type to make light call downs or shove this turn without the nuts I'd just triple barrel all of your flushes because KQ is essentially the top of their range here and that's not going to be a comfortable hand to call 3 streets with.