Bose Chaudhuri Hocquenghem (BCH) vs Reed Solomon (RS) Error correcting codes and sound transmission channel modeling
What channel model fits data transmission over air best, I guess distortion generated by speakers should also be take under account?


Disclaimer: I'm really not an Audio person. There's a lot of audio DSP engineers on here that probably have a far better idea of what's happening on an acoustic channel. But:


Frequency selectiveness will be pretty important. It's unlikely your phone speakers can go below 40 Hz, or far above 12 kHz.
Audio typically might experience a bad case of multipath
prepare yourself for what would be a relatively solid amount of Doppler if your communication partners, or significant reflectors, or the medium, are moving



  Is there a general study comparing BCH vs RS in different channels?


probably, hundreds. But: it's really a thing that needs to be compared under specific channel models, and since there are freely available implementations of both, as soon as you have a realistic channel model for your specific use case down, simulation should give you more application-specific results than any study might ever give you.

I'd really go for channel sounding, in your case; send a known signal of suitable bandwidth, record the raw reception, try to extract a transfer function from that (assume LTI, and verify that assumption). Change the environment/channel, and do it again. Do that ten times (and write a paper), and come up with a stochastic channel model (e.g. "we have this general amplitude response for the ideal single channel, we have x~(PDF) multipath components, and their delays and weights follow the XYZ distribution", and write a paper). 

Then write a channel simulator (at this point, I might, again, recommend GNU Radio, for which several channel sounders and channel simulators exist, but mainly for RF channels – but that's not inherent to its design, just to most of its userbase; obviously, write a paper), and test a few codes on that (and write a paper :))!