Ah, therein lies the problem, anonymous. Any time you shift attention from one pokémon to another, especially if you don’t explain the situation beforehand, you risk instilling a sense of jealousy in one of them. Yes, this happens even if the jealous pokémon is one of the nicest, most selfless you’ve ever worked with or if the jealous pokémon had been close friends with the one you’re affording more attention to.
With that in mind, in order to rectify the situation, you need to do two things. First, you need to explain clearly to your pokémon (both of them) that you’re not replacing either of them. You’re simply redistributing tasks. Of course, it’s also important that you offer this explanation without implying that your flygon is simply better suited to flight than your altaria. Otherwise, you risk provoking your altaria to “prove” that it’s just as capable of a flyer (by fighting your flygon again).
The second task will help you avoid this implication. What you need to do is, quite simply, spend more time with your altaria. Find something that it does best and work with it every day. Spend a little more time training it. Do everything you can to make it feel important to you or to make it feel as if you’re spending an equal amount of time with it as you do with your flygon. The more effort you put forth to make your altaria feel like a part of your team, the more your altaria can rest easy that its place hasn’t been taken by flygon. And thus, once you figure that part out, it will be less likely to instigate fights with its partner.
Likewise, your flygon may also be less likely to display dominance over your altaria, but I would also keep an eye on him and reassure him that your altaria is not a threat too.
Best of luck, anonymous.