As writing an answer to my own question, I came across this,
Plutarch, Life of Solon 26. 1 (trans. Perrin) (Greek historian C1st - C2nd A.D.) :
"He [Solon] also spent some time in studies with Psenophis of Heliopolis [in Egypt] and Sonkhis (Sonchis) of Sais, who were very learned priests. From these, as Plato says, he heard the story of the lost Atlantis, and tried to introduce it in a poetical form to the Greeks."
What is the connection of the Greek and Egyptian myths about Atlantis?
If there ever was one, we don't know what it was. Most likely, there never was one.
The only real original source we have for the story of Atlantis is Plato. He used it as an allegory to help describe his vision of the best way to run things politically. It was sort of his equivalent of Thomas More's Utopia. The society itself appears to be very maritime (like Greece and decidedly unlike Egypt). It doesn't look at all like a myth an inland river-centered Egyptian would come up with.
All other sources we have for the story came after Plato, and seem to be based on his stories. So the most likely (and currently favored) supposition is that Plato himself made it up. Even if he didn't, he might as well have, because that's all we have.
According to Plato the Greeks didn't knew of this story. The first Greek to learn about Atlantis was Solon, who stayed for some time in Egypt.
The story says that a wise Egyptian priest told Solon that there had been numerous cataclysmic natural disasters in the past, each time exterminating most of humanity. And that because of that, after the disasters humans would start building their civilizations once again from zero, having lost all of their knowledge. So the Egyptian priest tells to Solon that the Egyptians were wise to write history on the walls of their temples. Thus with ink that is waterproof they wrote on stone buildings that are fireproof and earthquake proof, in case yet another disaster happened, the history wouldn't be lost. (Think about all the hieroglyphics written on the walls of the Pyramids...) So eventually the priest says that a cataclysmic event did happened, and that lead the Greeks, who weren't prepared to loose their knowledge about the past, while the Egyptians retained it. And he goes on to tell one of the stories written on the walls to Solon, as an example. And that story, is the story of Atlantis.
Things to look for:
1- Has Plato ever used an allegory or utopia to describe his visions about some subject, in any of his work before or after the story of Atlantis ?
2- The date given by Plato for the fall of Atlantis (9000 years before the time of Solon, or 9600BC) under floods and fire is consistent with new research on what appears to have been a period of comet or asteroid strikes at the end of the Ice Age. This same period corresponds to great death rates of large animals and disappearing of some known human cultures in the Americas.
