You must learn a special skill to tame Blood Beasts. It is taught by a Blood-Soaked Tome of Dark Whispers, a guaranteed drop from Zul in the Uldir raid on Normal Mode or above (i.e. not LFR). Once learned, this skill is account-wide.
Appearance:
Location & Notes:
Located in Blood Gate, Zuldazar. Bloodbelly Flyers with three different IDs may be found around the Blood Gate area, but the majority of them have this ID.