Let's look at some facts that support Sylveon's typing.
Firstly, the name. Sylv- can be interpreted as a Latin root word for wood or forest. Since Leafeon already occupies the grass type, we can rule that rationale out. Sylv- can also be taken as a corruption of the word SYLPH. Sylph (or Silph) is a Greek mythos creature that embodies the element of air. Hence, flying type.
Next let's take a gander at Sylveon's design. Most people would have guessed Eevee's flying type evolution to have some sort of wings, however, there are many pokemon capable of flight or granted flying type status without wings.As a quadrupedal ungulate pokemon, we have only seen one other 4-legged flying type, Shaymin not including Arceus with Fly Plate, which seems to fly a lot like Santa's reindeer. Traditional westert kites are often adorned with ribbons and bows to stabilize flight. Sylveon's kite-like ribbons and bows also hint at flying type.
TL;DR Sylphs (as in SYLVeon) are mythological creatures of air; The bows and ribbons are like a kite's.
EDIT: Sylveon is also the lightest of all of the Eeveelutions. Just another bit of evidence to support this hypothesis.