I'm pretty sure that at least Eevee, Vaporeon and Flareon can have fangs as well, because they can learn the move "Bite" on level up, in which with bite, the target is bitten with "viciously sharp fangs". The fangs on Sylveon could be just for show, y'know. Or something. Not to say that it might not mean something, I'm just saying it might be just for show.
Hm, well, this is a thought, but:
Rainbow in the background.
The Eeveelutions don't exactly match the colours of the rainbow (lacking orange, adding black and brown), but they are close enough. I'm going out on a limb and guess that the Eevee mini-movie will feature rainbows to some extent, and that Ninfia will be connected to them somehow.
This has been proposed before, but I think it might be worth bringing up again. What if Ninfia isn't a standard Eeveelution, but rather connected to all of them? An overarching Eeveelution capable of either mixing the capabilities of the others or downright change into them à la Multitype (wholly or partially). Its typing could be Normal when in "Standard form", but change into the type of the mimicked Eeveelution when transformed.
Either way, if Ninfia can be connected to rainbows, both linguistically and via the movie poster, I'm beginning to doubt that this can be a coincidence. There's something with Ninfia and rainbows, maybe.