No, he can't fly. Or if he can he chooses not to for whatever reason. He was flying off in one of Bulma's capsule helicopter things and got shot down by the Androids.
I can't speak for the manga, but he never flies in the anime.
EDIT: A quick check of the Dragon Ball wiki confirms that he can't fly. He probably could learn, but he uses it as an excuse not to fight.
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