In the real world, humans have tamed horses and use them as mounts. Horses have very specific characteristics that make them a viable mount, such as size, back-strength, stamina, diet, behavior, etc. That is also the reason why we don't ride animals such as deer and zebras.
In my fantasy world (a world of hovering islands), humans have domesticated Species X to be used as flying mounts. Species X are feathered animals that have six limbs, four for land locomotion plus two wings.
What anatomical characteristics would these creatures need in order to be practical flying mounts?
- Mount: an animal that people ride in order to travel arbitrary distances
- Flying: capable of self-powered and controlled movement through the air
EDIT: If such a creature seems unfeasible, an answer stating so with proper arguments is as valid as any other.