I have premium, but there is no option to download DT in the store and the only option that could be DT costs money. I’m on 360.
Oh man, I’m on XBO but I had major problems getting the DLC for BF4. If you go to the Microsoft website customer service, they have a live chat you can use. You might have to wait 10 minutes, but it’s worth it as opposed to waiting for an ambassador(non Microsoft employee). They can walk you through what to do.
I had similar issue on Xbox one. Try turning of the game system and turning it back on. Start bf4 and go to the main menu. On the side where it advertises the new DLC and open the store in battlefield. Try to buy dragons teeth through the store in the game menu and it might download.