The ice age thing is an interesting idea, but doesn't really survive the Occam's razor test. (Not that that means it can't be true.)
The world's so-called pristine civilizations (the ones we believe developed without outside influence) emerged in river valleys where flooding was common and sometimes necessary for a good harvest. (The Andes civilization is an exception to this.)
It wouldn't take much leap of the imagination for storytellers to come up with tales of larger, more catastrophic floods. We human beings often deal with fear by telling stories about frightful things, after all.
Combine this with the idea that people in these early civilizations had no idea how large the world was, and the concept of a worldwide flood shrinks in significance compared to the way we think about it today.
Our imaginations may require the end of an ice age for producing a worldwide flood, but that's probably not how people in Mesopotamia, Egypt or the Yellow River valley thought about it.