The other way around is more plausible to me: the way we reconstructed dinosaurs was influenced by the corpus of representations we developed with dragons.

It makes less sense than imaginations running wild at the sight of crocodiles and dinosaur bones.

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.

Well, there's been a number of very large bird and reptile species that humanity has been in contact with since the dawn of man. Many of our forefathers were rather small compared to modern humans, and a gigantic serpent or amphibian would probably be outright terrifying for small early humans armed with rocks and spears.

I'm not sure about genetic memory, but human oral tradition is very old, and while I haven't heard about any evidence suggesting it predates modern humans, I wouldn't be surprised if there are stories that turns out to be as old as human language is.

Or found their skeletons.

It’s a very good possibility that the reason we think dragons lived in caves was because there are so many cave bear skeletal remains in caves throughout Europe.

Imagine finding a 12 foot long skeleton in a cave, or just a skull of an impossibly large animal, of course it’s a dragon!