Chinese dragons may be a better depiction of what could be the source of the myth. A Chinese dragon is like a flying snake, although I'm not sure they ascribe fire-breathing to it. But if you combine a flying snake and fire-breathing then there was an ancient device that looked very much like such a creature.

Some ancient armies used long cloth bags as flags or banners, to impress the enemies or maybe to signal the position of themselves for the allies to see. They filled the bags with hot air and the bags rose to the sky as contemporary balloons.

Imagine how it looked from the enemy side: an army is approaching and long snake-like things are flying about the mass of people. And you can glimpse some fire at the end that is close to the ground. Could it be a creature that breaths fire? And occasionally these things detached and flew up to the sky. Perfect dragons.