Even though garchomp cannot fly, almost all of its 4th gen pokedex entries state that it can. Its D/P and HG/SS pokedex entries say it can.
Diamond: When it folds up its body and extends its wings, it looks like a jet plane. It flies at sonic speed.
Pearl: It flies at speeds equal to a jet fighter plane. It never allows its prey to escape.
HG/SS: Its body is covered in fine scales that reduce drag, enabling it to fly at high speeds.
Its sorta a mystery why garchomp cant learn fly even though it can fly in the anime and alot of the pokedex entries state that they can. With this information, garchomp should learn fly but for some strange reason, it just cant.