How do you keep them all separate so they don't get these diseases? Are these diseases airborne or because of contact?
Depends on the disease. Some diseases float in the wind, others need actual contact, some are passed thru drinking water or feed, and others you yourself can bring in on your feet, hands or clothes.
It is best to keep chickens and quail at least 25 or more feet apart. Always wash your hands between the two species, change your shoes if you have walk in quail aviaries and are walking between the two species. Don't share cleaning utensils, water or feeders. If you just got done cleaning or raking out one of the areas, change your clothes. Just practice the best bio security as you can. I keep both chickens and quail and I have never passed anything to either of them. Chickens are not immune to things either, and if you quail have some funky bacteria or virus, you can pass it on to your chickens on your hands or clothes. So just be careful, and you shouldn't have a problem.
There is no guarantee that either of these two will infect each other, as many people do keep them side by side or even together. But for myself, it is just not worth the risk of either my chickens or my quail.