I think I'm not entirely sure what your asking, so I answered every way I perceived the question could be asking
If we think his shoving range is larger than his calling range and we get into this spot with Axs, then checking our nut flush draws is fine. Not for balance as such but just because we get more money in against worse hands so it will be more +EV.
But from the flop/pre flop, I wouldn't play to attempt to get into this spot with my nut flush draws, by playing it the same as my sets, in order to balance.
In this scenario, I think his calling range will be the same as or wider than his shoving range so I just shove the nut flushes. But that might not be true, which would make check calling better.
If your asking, would I check low flushes in this scenario as well... thats an interesting question. He is probably folding enough to bet river profitably, but if only better hands are calling, we are in essence turning our hands into a bluff, and it is more profitable to check showdown with hands that beat much of his check back range.
Its a question of what do we perceive his river range to be and what do we perceive his calling range to be as to what is best. Nothing to do with balance.