I think you can raise the nut flush and nut flush draw on this board some of the time, but I think there are too many people seeing a flop for raising a weak flush in opponent's spot.
At the river Villain should only be calling with the K high flush or better I think. There are so many more Axs flushes than all the other flushes. Hero is UTG raiser as well, so a hand like 85s or K7s is less likely. Also, some flushes could slow down on turn.
Calling down with A
4
seems like a blunder to me. Hero should primarily be betting 3 streets with flushes or bluffing with the nut flush card. If you hold that card you are blocking a lot of bluffs.
You actually really don't want to face 3 barrels with the king high flush, but you have to call it down sometimes, because otherwise your opponent will be able to barrel the lone A
too much. If we give Hero a loose range of Axs, KTs+, Q9s+, J8s+, T7s+, 96s+, 85s+, 75s+, 64s+, and 54s. With holding the King high flush we beat 20 and lose to 12. The weakest flushes are checking back on the river probably and most of those hands aren't always being played from an UTG player.
If UTG player plays something like A9s+, A5s-A2s, KTs+, QTs+, JTs, T9s, we are in even more trouble with a king high flush.