Yes, a license must be obtained. I have the quote from Florida Fish and Wildlife Conservation:
"Persons interested in propagating game birds for commercial or private use must first obtain a game farm license from this agency. The cost of the license is $50.00 per year."
I haven't bought one yet because my seven quail hatched only a week and a half ago. I think there are specific regulations for non-native species of quails. Mine are bobwhite, so there aren't many regulations.
I would be interested in bobwhite and/or button quail. I would still need the license for either? I would be a hobby seller more then considered a "farm seller". I dont really have a huge commercial farm.. I live in rural residential.
Most states where a game bird species is native and/or introduced (i.e. Common Pheasant, Hungarian Partridge, Grouse) will require a permit to sell. Some states even require one if the species is native to the US; example, my state MO - needed for the various western quail species. Best bet to check your local regs before purchasing a wild species.
I wouldn't think Buttons would be, they are Asian after all and seen in pet stores right along side other cage birds. I have never seen record of any wild breeding colonies of the species in North America and being so small, they really shouldn't be considered "game birds" (they are, but not in the actual shooting sense!!) according to reading those docs.