K9 appeared more-often-than-not between The Invisible Enemy (1979) and Warriors' Gate (1981). He wasn't in every story, though: Power of Kroll is set in a swamp and has no K9 (he's sink). City of Death was largely filmed in Paris, and it wasn't economical to take the little tyke with them.
After he was binned off in Warriors' Gate, they tried to give him a series of his own, explaining that Sarah Jane was sent a K9 in a box by the Doctor. The series "K9 and Company" only ran to a pilor episode, "A Girl's Best Friend", which is a real hoot but it not really anything to base a series upon.
K9 got a scene early in The Five Doctors, warning SJ that she's in danger (which she was, of course). He cropped up in a couple of new series DWs, and every-now-and-then in the Sarah Jane Adventures.
K9's got his own series now, in which he can indeed fly. I haven't seen any of it though.
I don't see him returning: he's done his bit for the new DW, and the new DW has helped promote him in order to make the Aussie version of K9 a realistic goer.