It wasn't my experience that flute affected facial growth, though I only began playing when I was 12. My CFD was set off by something else.

Have you considered looking up pics of your favourite flutists and seeing for yourself? Most professional flutists probably began very young. I think at most the muscles around the mouth would see some hypertrophy. Given that proper tongue posture was maintained, the aesthetic effects of such would likely be minimal

It shouldn't.  I see sometimes they have beautiful lips.  

Playing the saxaphone, trombone, clarinet, trumpet, tuba, and digereedoo (especially) help airway and players have less incidence of obstructive sleep apnea (OSA) than others.  I heard once  on here that violin or viola players (who tilt to one side) may have something going on there weird.  I don't buy that.  

Oboe, bassoon... double reed instruments are supposed to be great.  I wouldn't touch those personally.  The excellent, professional players get frog necks.  

I heard someone say that clarinet players get buck teeth.  I played.  I don't think my teeth were bucked... but even if they were... it probably helped give me a nice, forward maxilla... It was not problematic for me & my maxilla was great for a long while (retruded a bit with Mewing attempts).

Survival instincts kick in.  I personally know someone with a small airway who gravitated towards the saxaphone and later the digereedoo.  You could use PVC pipe and beezwax to make a digereedoo.  It wouldn't sound as awesome as real wood... but it would only be $3-5 USD.  Plus, if someone asks what you're doing... you could say, "none of your beeswax."  lol