I'd recommend you breed for better IVs, to begin with, because that noivern has terrible IVs in Speed and Special Attack especially -- those two are its most important stats.
I'd also recommend you consider actually EV training it to mazimize speed and special attack. Beating wild woobat and noibat any cave yields speed easily, and SpAtk can come from slugma (not magcargo) and numel, also easily found in Pyrous mountain.
As for moves, Ideally you would want Dragon Pulse, Hurricane, Boomburst and Flamethrower.
Hurricane and Dragon Pulse can be tutored and will also be learned naturally at higher levels. Air Slash is an acceptable alternative until you get Hurricane, but it is very weak, especially since even a fully invested Noivern has rather average SpAtk. Roost and Super Fang would work better on a bulkier Pokemon, but I guess Noivern may be able to pull it off. It's not very good later in the game, for sure; you'd want straight power then.
Flamethrower is something you'll have to wait until a later gym to get, though. Until then, Roost or Super Fang could both work.