The rules for riding animal companions limits the animal companion to grounded movement unless it has the "mount" ability.
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You or an ally can ride your animal companion as long as it is at least one size larger than the rider. If it is carrying a rider, the animal companion can use only its land Speed, and it can't move and Support you on the same turn. However, if your companion has the mount special ability, it's especially suited for riding and ignores both of these restrictions.
However, to my knowledge not all megafuana companions have stats. In the case of the roc, we are told that a young roc has the stats of a bird, but we are not told the stats for a mature roc. Thus, we don't know if a mature roc has the "mount" ability.
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Roc: Use bird statistics for a young roc.
Now, there are several reasons to think that an adult roc should have the "mount" trait, or otherwise be able to fly with a rider. This is not only logical, given the size of an adult roc, but even stated in the fluff
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Particularly skilled druids or rangers might capture and train a roc to serve as a flying mount
From a RAI perspective, though, what is most relevant is the wording for the mammoth lord's trampling charge feat. This action requires that the mammoth lord is riding their mount, and clearly indicates that the animal companion can use special modes of movement, such as flying.
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You urge your mount forward, trampling enemies in your path. You command your mount to Stride up to its Speed (or to Burrow, Climb, Fly, or Swim, if it has the corresponding movement type)
This leads me to my question. Seeing as everything seems to points towards an adult roc being capable of flight while ridden, is there anything RAW that undeniably leads to this conclusion?