All my quail chicks were a little skittish, although they would more than happily approach my empty hand, expecting some treats! It was adorable. (Chicks should normally imprint on you if there's only a few of them, although I'm not sure what's happening to the little guy.)
When they grew up, I spent less time with them because of school. They became less tame when I would approach them, one in particular would very quickly dash away from my hand if I were to change the water. Now she's tame enough to only jerk back when my hand approaches instead of running away, and she will allow me to pick her up for a bit before wanting to go back. Most of my other quail are quite tame aswell and when I come to pick them up, they won't run away, but instead allow me to pick them up, even my roo is quite tame.
I spent more time with them, just hanging around near the cage so they can see me. I throw their favourite treats into a cage (mine love clovers, boiled egg, grass, noodles, rice, fruits, veggies, baked eggshell, budgie seed mix, bugs, etc.), and let them eat it, then put the treats in my hand and let them eat from that. Sometimes I'll pick them up, pat them, talk to them (hehe), then if they start to get anxious, I'll gently put them down before they fly down themselves.
Quail love to eat, so use that to your advantage.
You'll know if they're really tame if they are willing to eat treats from your hand whilst you're holding them.
It may take some time though, as quail are generally skittish because they are prey birds, but coturnix quail are one of the calmer species so it should be a little easier.
