We know they had caanite slaves, and slaves from pretty much everywhere. There were enough caanite slaves that they had ghetto settlements that left records.
However it's not the mass slavery as presented in stories, that's a more modern addition to the story.
As for Moses, Joseph is the more exciting part, that probably happened during the Hyksos peroid, where after the foreign invaders were thrown off, the egyptians destroyed all records of them. Which, the important part of the story, that a semite from the levant became a senior minister, is the interesting part of the story. As that is a period where Egypt was conquered by, probably, an alliance of merchants, foreignors, mercenaries and nomads, but definitely, semites form the levant.
Who after they were overthrown, either fled or were reduced to slavery.
And here we have slaves leaving egypt, who claim to have been invited to egypt and moved in, after one of them got a senior position in the egyptian government.
Um, anyway, acouple years ago, I could have answered this question really well, as I read two books on it. However that was two years ago. Maybe three.
Anyway, from memory, there is lots of evidence that there were Canaanite slaves in egypt at the suggest time, but none of moses' rebellion or plagues.
And that slavery wasn't on the thousands of slaves under whip-masters, but household, agricultural, etc, slaves like every other ancient part of the world have. The idea of thousands of slaves in intolerable conditions comes from a misunderstanding about how pyramids were built and post-slavery european imaginations of what slavery was like, and hell, from US chattel slavery centuries later as our image of slaves in egypt is more from pictures, films and etc than the bible.