You must complete mission 24 before you can complete the entire quest. So if you just completed mission 15, you still
got a ways to go before the dragoon is unlocked. So yes, wait till chapter 3, like Fun said.
" * After you have gotten both the Dragon Helm and Armor, return to Mylesia, Idorf and get info about the Sword of Tiamat.
* Get the Dragon Scale and Divine Dragon info at Fair Heights, Elaine after mission 21.
* After mission 24, your unit leader will fight a dragon in Celesis, Pinneg. You will receive the Sword of Tiamat as a prize."
I do hope that helped! Good luck with your game!