Are you
Baked Alaska?
I am a body part in flames
Baked Alaska is lit aflame
The earth and I move the same
Alaska is a territory on planet earth
I am a dessert without tea
Ice and tea normally don't go well together (unless it's iced tea) (Not too sure on this one)
When it comes to cake, I'm not easy
Baked Alaska is rather difficult to make (compared to other cakes) (also, baked ice!)