A Stone Flyer is not too far removed from it's common wolfen cousins. It prefers to attack in packs, secure incapacitated, or dead, prey and then disappear into the earth with it's trophy using it's innate Earth Glide ability, which that makes it a well sought after mount in places like the Underdark, though it's natural Evil disposition makes it a tricky ally to keep.

If willing, or if domesticated, a stone flyer can be used as a mount capable of taking flight if not carrying cargo above 335 pounds. Under these same conditions a stone flyer can also extend it's Earth Glide trait to anything in contact with,, or connected to, it (like a familiar in the shoulders of a creature riding it).

TRAINING YOUR EVIL DOG

Many an adventurer would jump at the opportunity to have an exotic creature like a Stone Flyer at their side. But these are evil creatures, so how would they even go about? The same way one would bargain with a drow smuggler in the surface, or slightly inept duergar trying to scam surfacers in the Blade Bazaar of Gracklstugh

Personally i would recommend a limit of 2 starting attempts per player at a DC 22 Charisma Check for adults (Animal Handling under normal circumstance, or anything other Charisma check if the PC speaks Primordial, therefore cna hold a conversation with the target), or DC 15 for a pup, to convince them to stick with the character. Then 6 work weeks worth of training it, to be an effective mount, by someone good enough at it, which means an NPC or a player that manages to pass an DC 18 Intelligence (Animal Handlig) check for first 3 weeks of training, at which point failing in the check just delays the training by a week