The trick is that "some notion of a dragon" is incredibly vague, with "dragons" sharing very few commonalities between cultures. A European wyvern and Quetzalcoatl are almost nothing alike, yet people consider them both "dragons."

>Is it possible that these are based on inherited memories, patterns, insticts of dinosaurs?

It is possible that these are based, at least in part, on the discovery of dinosaur fossils, but humans didn't even evolve until the dinosaurs were long dead. So even if it were possible for "inherited memory" to include visual memories it wouldn't do so for dinosaurs.

Why should inheritance stop at species boundaries?

It isn't a matter of "species boundaries," which aren't even really rigidly defined, so much as time, complexity and information compression.

It doesn't seem likely that whatever primitive mammalian ancestor eventually evolved into primates, and then into humans, carried within it a coherent enough visual and behavioral memory of dinosaurs to have survived so many generations of mutation, eventually informing the modern idea of "dragons" as winged reptiles.

And again, it isn't even true that there is a cross-cultural concept of "dragons" to begin with. It's a eurocentric myth, in that it assumes a Western concept of a "dragon" to be the default, and ignores any other cultural context in order to fit their mythologies into that mold.