Honestly I do not believe there is any realistic way for GameFreak to portray the aesthetic effects of Doduo and Dodrio flying. Neither evolution are equipped with wings, which would lead to the 'running effect' as the most realistic way for each evolution to fly, as I believe staying still would look even less realistic.
Now that we have entered the realm of 3D in the Pokemon world, I'd imagine (like previous 3D Pokemon games on consoles) that we'll most likely be able to see our Pokemon after they've used the move fly, instead of them disappearing, which means Sky Battle or not, we'll be seeing Doduo and Dodrio fly, and it will not look so ordinary.
I'm glad I have played previous 3D Pokemon titles to have experienced this already. I'm prepared to face Doduo and Dodrio running on air.