I thought I got my barding from the moogle, but I realized that I didn't click "take all" from the mail. When I tried to change the barding on my chocobo it was just not there. So, I decided to go back to the moogle, and clicked on opened mail, I clicked through all the mail and saw that on my chocobo barding gift I didn't click "take all" and there it was.

Hope this help someone