Nice out-of-the-box idea. I definitely like it, seen the series several times and I really wish the universe of it would continue to expand.
There are two main concerns.
1. I wonder how copyright would go. As far as the IP goes it's fairly old-ish yet Nickelodeon makes a point to keep airing it simply because it is amazing.
The main concern would be not even on the content but the behind-the-desk-paper level.
2. On the negotiation level I think the main issue with Aang would be that he does not fit the setting and that he's anti-violence while superheroes in general need to punch things. The point of the avatar series which I'm sure all of us who love it already know - is that despite all his power he has mostly been trying to avoid combat and training for one battle that he simply could not avoid.
The Injustice setting - and the game itself - is wanton violence which the Aang character strictly stands against.
I do so love this idea though, it's fresh.