Here's another long shot. Are you
eyes?
I am a body part in flames
Eyes can burn if you get something in them
The earth and I move the same
Both are spherical and can rotate? Not a solid explanation
I am a dessert without tea
Most things that are iced (also a bit ofsince 'ice' sounds very much like 'eyes', also a stretch) would be considered desserts, but not iced tea
When it comes to cake, I'm not easy
It's not easy to ice a cake?