When two waves, propagating in a linear medium, interfere with each other, the amplitudes of individual points within the region of interference could add or subtract, but this does not affect the flow of energy.
We can show it in a simple example below:
Point A is in the region of interference and its amplitude will be affected by both waves.
Point B is beyond the region of interference and should not be affected by wave S2. This is because the amplitude at B is defined by a superposition of the two waves, i.e., it has to be the sum of S1 and S2 at point B. Since the amplitude of S2 at B is zero (or negligible), the amplitude at B is affected by S1 only.
The same could be said about all point of wave S1 beyond the region of interference. If so, we have to conclude that S2 would not affect S1 beyond the region of interference and therefore will not change the flow of energy of S1.
We could come to a similar conclusion, if we took into account that the waves don't get reflected while propagating in a uniform linear medium, which means that no energy is coming back and, therefore, it should continue moving forward, unaffected by other waves in that medium. The sound wave moving in the air will be reflected by a wall, but not by another sound wave.