Sort of in 3.5e, not so much in 4e or 5e. While it's widely know for the potential for abuse in theory/totally premissive games the feat Leadership can got you a flying mount as a cohort at higher levels. Likewise the web-published feat Wild Cohort can do the same thing. Although I think that's at slightly higher level (for anything better than a giant bat) but with a better 'recovery after loss' mechanisim.