He doesn't seem to have any flight feathers. Was he clipped before you got him? If he was clipped, then he won't be flying at all until he molts - 4 or 5 months more at least. The tail feathers could have been accidentally pulled out or broken if he fell trying to fly.
If he was never clipped, and simply hasn't grown the flight feathers, or had some and lost then, then something is wrong. Polyoma virus (older budgie books call it French molt) will cause baby budgies to lose their flight and tail feathers. If this is the case, there's no cure but he can still live a fairly good life with some special care. I would stronly recommend you get him to vet to be tested so you know what you are dealing with. Also if he has Polyoma, it is very important that you don't expose him to other birds, especially a baby birds, unless they've been Polyoma vaccinated, since it is contagious.