Oh this mini-game....

You need to obtain the feather of the flock o speak to them.

And they appear in:

Eruyt Village
Jahara
Archades
Dalmasca Estersand
Rabanastre
Balfonheim Port

When you get all of them, Return to Giza Plains. You will get 2X Hi ethers for your troubles.

However, for every Bird you get, you a prize! for Rabanastre you get a Diamond Sword.

TIP: Use the shortcut (North end) To Ambush it. You have to compleate the Eruyt Village one before this one.