A lot of people in Egypt were slaves. Some of them came originally from Egypt - often children sold into slavery by poor families. Others were sold from other countries into slavery in Egypt. A lot of people from Meroe and Kush, south of Egypt, were slaves in Egypt, and a lot of people from Libya.
The most famous story about Egyptian slaves is the one in the Bible about how the Jews were slaves in Egypt, about 1400-1200 BC. Because the Egyptians had just conquered Israel at this time, probably many Jews were enslaved about this time. Then when the Egyptian New Kingdom collapsed, they stopped being able to enslave the Jews.
To find out more about Egyptian slaves, check out these books from Amazon.com or from your library:
Everyday Life in Ancient Egypt, by Lionel Casson (revised edition 2001). Not especially for kids, but pretty entertaining reading, and Casson knows what he's talking about.
Private Life in New Kingdom Egypt, by Lynn Meskell (2002). A little more specialized and harder to read.