A Foo Fighter is not a vehicle per se, but it walks and quacks like one. 

Instead, it is a Samsaric Manifestation that represents a singularity in Spacetime, meeting only the bare logical minima to interact with material reality. They appear as points of incredible light, but this is merely what something "looks" like when all the variables that left null. Their inhabitants are similar manifestations in a humanoid form. 

Patterned Flight & Movement

Patterned flight is an observed phenomenon of Foo Fighters, taking place when entering and exiting material reality. The appearance of movement over time is simply the "splash" of this transition - none is actually necessary for them to enter material reality, since they can be inserted wherever they please. But as you can imagine, it's fucking disorienting to manifest physically if you're not a primarily physical being, so they are often just a little bit off from their target and need travel capabilities.