There is nothing you can do about mosquitos (other than what you'd do vs them in general, like in your yard -- dump standing water, etc) although if you shut your chickens int he coop at night, windowscreen on the windows will reduce how many mosquitoes get in to bother the chickens at night.
Flies are mostly coming from breeding in damp poo, so the drier and cleaner and non-mucky you can keep your coop and run, the fewer flies you'll have. A mud problem tends to also become a fly problem; damp hay or straw or etc in the run does the same. For damp run fixes, see the link in my .sig below.
To some extent you just ARE going to have more flies when you have chickens, though.
Good luck,
Pat