Your theory of being part of a Flying type is okay. But I actually completely disagree with your explanation about the Dragon Type.
First up, Ninfia doesn't look at all to a dragon type (if we except Altaria). I really doubt of it.
I don't know why is people are obsessed by Ninfia's little cute teeth since some Eeveelution has teeth. For exemple,
Glaceon has.
For the "fire" move in the CoroCoro pages, I think it's just sort of a Fire type's. Since Togepi can have Flamethrower, all is possible. It could have been attack such as Metronome, Copycat or Me First too. This cannot be count as a hint.
Finally, going my logic, I really don't think this sort of Eeveelution is appropriate for a Dragon type. It's too much gorgeous and elegant to be revelant...