Here is an idea: Natsu's home world is overflowing with magic. Maybe flames and more generally every object there has magic inside it from the very beginning. This would explain why, as user30104 mentioned, magicians can collect magic from their surroundings. By his upbringing as a Dragon Slayer, he can eat fire insofar that he directly absorbs all magic left in it.
In conclusion, in the almost magicless Edoras, there is no intrinsic magic in any object, yet alone flames, so Natsu couldn't just use fire as free magical batteries there.
It should also be noticed that Natsu's power increases a lot during the course of the manga and the little bit of magic that he can gain by eating flames may be enough to beat up some thugs, but not enough for the threads of Edolas and later.