They're pretty picky so you might as well feed them fruits and veggies in a pan so you can throw out what they don't more easily. They will require digestive grit given to them to properly digest anything that isn't a poultry crumble/pellet (they don't need it with game bird/poultry feed because that is water soluble).
They only veggies/fruit I'm aware of that are bad for them are avacados (They are poisonous for quail so i never tried feeding them to my chukars) they will like some things more than others so just experiment I mostly only feed my gamebirds fruits and leafy greens when i give anything so I can't be much more help. You should also search around the BYC archives to find more info, just about every question you could think of has been asked and answered there.