
Finoan |

Just to be clear, are you mixing up familiars and eidolons there? Your initial post sounds like it's talking about familiars.
I was reading the original post as meaning a Beast Eidolon in the shape of an oversized owl (I have one in the shape of a chicken, so I can relate), and a Demon Eidolon which would be close enough to a Devil like an Imp that it would pass the flavor check.
But to be more complete:
An Eidolon is a feature of the Summoner class specificially. It isn't going to have a fly speed until you give it one temporarily with Evolution Surge or permanently with Airborne Form. (And only Airborne Form is going to end up listing the fly speed in Pathbuilder since the app doesn't track temporary spell effects.)
Pet is a general feat that anyone can take. It does have the Flier ability available.
Familiar is a feat that several spellcasting classes and a few Ancestries can get. They use the base rules for Pet and have additional options. So they can also get a Fly speed from the Flier ability.
For both Pet and Familiar, you need to select Flier in the Pathbuilder app in order for the fly speed to show up.

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Beast eidolons have a unique opportunity for you to create chimeras as they evolve. Naturally, they do all start off flightless so bird eidolons are a bit awkward so you might want to consider what might gain wings later on. My vote would be a tarantula. What's worse than a 10 foot tarantula? A 10 foot tarantula with wings.