I can answer this question. I have Button/King quail in a large outdoor pen ( 8ft x 20ft ) with my bobwhites and valley quail. They all get along just fine. When I first introduced the buttons there was a day or two where there was some getting to know each other but now the larger quail treat...
https://www.ebay.com/usr/3313wilson
and
https://www.ebay.com/usr/pomme5764
are the two sellers I bought the eggs from, they are still incubating so I don't know the results yet but the second seller had about a 30% non-fertile rate. The box was pretty mushed up so I think it was a shipping...
I just got 85 butler bobwhite eggs from two sellers on ebay. I am hatching them now. If you can't find any I'll send some your way once mine start laying if you're still interested.
line the sides of the pen with 2ft tall 1/4" hardware cloth. Keeps them safe from predator hands at night. Pen also MUST be covered or they will fly out and/or get eaten.
These two guys have been adorable but with the onset of their curl feather they have decided that two of my hens are the target of their hormones. They need to go to a place where they'll have more female ducks, which I have a shortage of.
I am in SW Washington State/Portland OR area.