Over the few years we have kept them, a handful have managed to fly out of their pens, usually when my daughter was catching them so that we could give pens a really good clean. They seem calm one minute and then gone in a flash. On two or three occasions, they have disappeared and we haven't been able to catch them. One male was gone for about 3 days .... thought he had probably been eaten ... then daughter came dashing back to the house and he had made his way home and was in one of our open hen coops .... as it was daytime they were out free ranging. All others came tootling back and circling their pens to get back in after a few hours.
If you have a spare coop of any description you could try leaving the door open, with food inside and hope he returns of his own accord. Put the coop next to the quails proper home. If it helps, we keep an old bath towel handy if we have any fly-aways and we sneak up and throw the towel over them when they return. They tend to be so fast and fly away again, otherwise, as you approach. My 10 year old is expert at catching them now and the neighbouring farmers know what she is doing when she runs across their fields with towel flying.

Bonkers.
Good luck