chicken wire is fine for the sides, but coturnix will stick their heads through it (and can be torn off by predators happens more than you think). I think Saddina was meaning as their walking wire, chicken wire would be too wide for them to walk on but if you're planning on putting them ON the ground ground wire is no issue
Quail can do very well with chickens provided the coop or enclosure is big enough that they can have their space from eachother.