A Bird's Tail

First feather:
Spires of Arak 45.78, 53.59 Beneath Alignment Controls

Second feather:
Talador 29.56, 29.54 West of Shattrath

Third feather:
Nagrand 83.82, 19.38 On a peak/ledge

Fourth feather:
Frostfire Ridge 42,67 On a small hill above Frostcave
This appears to be bugged for Horde users right now. The feather is actually located on a hill right above the Frostcave, but will phase out if not clicked quickly. If you're just right with your approach and have max mount speed, it's possible to land and loot before it phases out, but difficult. Again, this seems to be a Horde-only issue.

As Bloodys pointed out in comments, getting invited by someone who has no garrison/shipyard, and them syncing seems to be the best workaround until a hotfix is deployed.

/way #542 45.78, 53.59 Feather One Beneath Alignment Controls
/way #535 29.56, 29.54 Feather Two Just west of Shattrath
/way #550 83.82, 19.38 Feather Three On peak in Nagrand
/way #525 42.03, 67.52 Feather Four On small hill outside Shipyard

This is all in Draenor, so if you're like me and can't find it in Outland Nagrand... DOH!
Happy hunting!

This guide will help you find the feathers needed for A Bird's Tail. Please note that some feathers may be affected by bugs.

First Feather:
Location: Spires of Arak
Coordinates: 45.78, 53.59
Description: Beneath the Alignment Controls
/way #542 45.78, 53.59 First Feather

Second Feather:
Location: Talador
Coordinates: 29.56, 29.54
Description: Just west of Shattrath
/way #535 29.56, 29.54 Second Feather

Third Feather:
Location: Nagrand
Coordinates: 83.82, 19.38
Description: On a peak/ledge
/way #550 83.82, 19.38 Third Feather

Fourth Feather:
Location: Frostfire Ridge
Coordinates: 42.03, 67.52
Description: On a small hill above Frostcave
/way #525 42.03, 67.52 Fourth Feather