Double move fly, run fly...

[nogoodscallywag]

Can a naturally flying creature double move in a straight line horizontally?

[Mathwei ap Niall]

Yes they can double move but they cannot run.

[Ravingdork]

Why not, Matt?

[Are]

Flying creatures can run. They exception is those who fly via the fly spell (and other spells and items based on it), since that spell specifically states you can't run when using it.

[Red Wullf]

Are is spot on. Sadly, PFRPG seems to have neglected to include the details of creature movement modes that 3.5 had. Perhaps they'll fix this, or at least FAQ this someday. See Movement Modes under Special Abilities in 3.5. "A creature can use the run action while flying, provided it flies in a straight line."

[Majuba]

No need to specify - run does not restrict to land speed.

Are is correct.

[Kobold Catgirl]

Yeah, Pathfinder is shamefully vague when it comes to how basic movement types work. That needs an errata way more than "latest powerful martial ability", if you ask me. :P