Bird mounts are epic mounts, that are obtained from a variety of different ways.
[Corrupted Egg of Millagazor] is a reward for completing [Glory of the Firelands Raider].
[Felfire Hawk] is a reward for completing [Mountacular].
[Reins of the Raven Lord] is a rare drop from Anzu in heroic Sethekk Halls.
[Ashes of Al'ar] is a rare drop from Kael'thas Sunstrider in The Eye.
[Flametalon of Alysrazor] is a rare drop from Alysrazor in the Firelands.
[Smoldering Egg of Millagazor] is a rare drop from Ragnaros in the Firelands.
[Voidtalon of the Dark Star] is contained in the object "Voidtalon Egg". The egg is found from stepping into an Edge of Reality, which rarely spawns all around Draenor.
[Clutch of Ji-Kun] is a rare drop from Ji-Kun in Throne of Thunder.
[Solar Spirehawk] is a rare drop from Rukhmar in Spires of Arak.
Voidtalon of the Dark Star
[Brilliant Direbeak] is a reward from  Direbeak Reunion.
[Predatory Bloodgazer] is a reward from  Bloodgazer Reunion.
[Snowfeather Hunter] is a reward from  Snowfeather Reunion.
[Viridian Sharptalon] is a reward from  Sharptalon Reunion.
[Shadowblade's Murderous Omen] is a Rogue-only quest reward from  Hiding In Plain Sight.
Shadowblade's Murderous Omen
[Reins of the Dark Phoenix] is purchased from guild vendors for 3000 if the guild has completed the [Guild Glory of the Cataclysm Raider] achievement.
[Reins of the Corrupted Dreadwing] is purchased from Dawn-Seeker Krisek <Order of the Awakened> in Tanaan Jungle at a cost of 150,000 upon reaching friendly with Order of the Awakened.
[Mephitic Reins of Dark Portent], [Bloody Reins of Dark Portent] and [Midnight Black Reins of Dark Portent] can be bought once [Power Ascended] is achieved for Assassination, Outlaw and Subtlety specializations respectively. Zan Shivsproket sells them in the Hall of Shadows for 1000 each once the quest mount is obtained.
Mephitic Reins of Dark Portent
Bloody Reins of Dark Portent
Midnight Black Reins of Dark Portent
[Reins of the Dread Raven] is a flying mount included in the World of Warcraft: Warlords of Draenor Collector's Edition, or can be bought as part of a bundle from the Blizzard Store.
The subject of this section did not make it out of the beta stages of Mists of Pandaria.
The Stormcrow is a bird mount that was datamined from the game during Mists of Pandaria. It has never been implemented, but does have a miniature version that is available as a companion pet.