Yes, because it’s a “force” (not a creature)
The key word here is Force. An unseen servant is not in the same class as, say, an incorporeal being under greater invisibility. It is, rather, a spell-created force effect that the caster controls via commands…rather like a simple automaton.
As a spell-created force-effect, it doesn’t truly have any “movement type” at all — rather, it merely has a speed which determines how quickly it can move from one place to another.
Unseen Servant can be thought of Mage Hand, Programmable Edition. It can do anything anywhere anyhow, so long as it is within the parameters of the spell…and by this, that includes flying.
By the way, as a total side note, if you play something that can get your own weight under 20 lbs though Reduce Person or other means, your Unseen Servant can carry you, too, as it flies about.