So I'm in a D&D 5e campaign and I'm curious about this because there's some debate in my current campaign about travel mounts, particularly Griffon vs Magic Carpet. A person in our group thinks that Griffons are better than magic carpets for traveling. I'm curious as to how long you can ride a Griffon or any mount for that matter, before needing for it to rest or eat?
The DMG addresses this on p. 119 (or here on DNDBeyond), under the section titled "The Sky":
Flying by spell or magic item works the same as travel on foot, as described in the Player’s Handbook. A creature that serves as a flying mount must rest 1 hour for every 3 hours it flies, and it can’t fly for more than 9 hours per day. Thus, characters mounted on griffons (which have a flying speed of 80 feet) can travel at 8 miles per hour, covering 72 miles over 9 hours with two 1-hour-long rests over the course of the day. Mounts that don’t tire (such as a flying construct) aren’t subject to this limitation.
As stated: Mounted flying creatures can fly up to 9 hours a day, plus two intervening 1-hour rests.