Is there a reason for that? I know how that applies to French horn, but not necessarily flute.

As a woodwind player, whenever I perform on flute, I prefer to be on the left side from the conductor's perspective. My body is more open to the audience and I feel like I can see the conductor better.

But regardless of which side I sit, I'm blowing straight at the conductor and the embouchure hole is where the sound comes out.