I will answer this in two parts, concerning historical tradition and actual historical documents.
Historical Tradition and Writings
None of the stories from the Hebrew Book of Names, which you know as the "Exodus" are found either in Egyptian sources or in later Greek sources describing Egyptian mythology with the exception of the account of Manetho. The account of Manetho, a 3rd century BC Greek writer, is called the Aegyptica and is purported to be based on old Egyptian history. In addition to Manetho's book we have a response attributed to "Flavius Josephus" which is a critique of Manetho's book. In the critique, the author seems to acknowledge the basic facts of the account as being true while denying various minor aspects. Manetho's account of the Hebrews is a long discursion from his main topic which is on the kings (pharaohs) of Egypt. We do not have the full original text of the Aegyptica, but only later epitomes, such as those by Syncellus. The account in the "Josephus" work, Contra Apionem is most detailed, so I will paraphrase it here:
Tutimaeus. In his reign, for what cause I know not, a blast of God
smote us; and unexpectedly, from the regions of the East, invaders of
an obscure race marched in confidence of victory against our land. By
main force they easily seized it without striking a blow; and having
overpowered the rulers of the land, they then burned our cities
ruthlessly, razed to the ground the temples of the gods, and treated
all the natives with cruel hostility, massacring some and leading into
slavery the wives and children of others. Finally, they appointed as
king one of their number whose name was Salitis. He had his seat at
Memphis.... In the Saitian district [ie the Sethroite Nome] he founded
a city and named it "Avaris" according to ancient traditions...[list
of kings follows]...These six kings, their first rulers, were ever
more and more eager to extirpate the Egyptian stock. Their race as a
whole was called Hyksos, that is king-shepards.... Some say that they
were Arabs. In another copy the expression hyk, does not mean "kings"
: on the contrary, the compound refers to "captive-shepherds"...These
kings whom I have enumerated above, and their descendants, ruling over
the so-called Shepherds, dominated Egypt, according to Manetho, for
511 years. Thereafter, he says, there came a revolt of the kings of
Thebes and the rest of Egypt against the Shepherds, and a fierce and
prolonged war broke out between them. The shepherds were defeated and
confined in Avaris. Avaris was besieged to no avail so a treaty was
made by which the shepherds would depart Egypt. The Shepherds with
everything they had numbering 240,000 people then left Egypt and
journeyed to Syria. There, fearing the Assyrians, they built a city in
Judea called "Jerusalem".
The only documents thought to be relevant to Hebrews in Egypt are the Amarna letters, which are clay tablets found both in Assyria and in the royal palace of Amarna in Egypt. These are diplomatic letters and in numerous instances refer to the habiru occupying the region currently known as Israel. In some cases there are Egyptian writings which refer to apiru and it is believed to refer to the same people. The heiroglyphics for this word are:
In addition to the Amarna letters there are some historical inscriptions involving wars in the Levant, such as the famous Battle of Kadesh inscriptions, however, in these inscriptions identification of the Hebrews are much more conjectural.