Where can I find a Dragon Plate in Pokemon X or is it not possible because there is no Dragon plate?
The "Dragon Plate" which is actually called the "Draco Plate" can be found on Route 22 in Pokémon X and Y.
It is located near the top of the waterfall by the Chamber of Emptiness. Note you will need a Pokémon with Surf and Waterfall in your party to obtain it.
For more help getting it click on this video here.
Hope I helped :)
It is possible.
You go to route 22, and then after that:
>Beyond Chamber of Emptiness - Requires Surf & Waterfall -Serebii
The Draco Plate can be found near the top of waterfall by the Chamber of Emptiness on Route 22.