Something I hadn't realized before when I was re-reading ancient magic: in the section on Adamic language it places Hamitic as being the language of Africa- this is in fact not part of any actual biblical lore that would have been recognized in the middle ages as the tower of babel was centuries after the flood and Noah's sons, but instead is part of the American justification for black slavery, in which Noah's curse on his son Ham to be slaves of his two brothers and his descendants slaves of theirs is assigned to the modern racial groups. The areas listed in the bible as being settled by Ham and his descendants would have been in the fertile crescent of Asia, not Africa.
The history of the curses of Ham and Canaan is complex and unpleasant: best start reading Curse of Ham.
AM p.12 has "... Hamitic, named after Noah's son Ham, from which Egyptian and Coptic has descended; ...".
This would not make Hamitic "the language of Africa", of course.
Still, listing Egyptians as descendents of Ham, or their languages as descended from 'Hamitic' would not fit with "any actual biblical lore" either.
Ham by Genesis is the father of Canaan, so would be the forefather of the people descending from him. Ethiopian legends and Oriental scholars have first some Ethiopian people descend from Canaan, then other people of Africa. At least the Nubian Kings of Kush ruled in Egypt as the 25th dynasty - but I am not aware of any medieval scholar calling Egyptians or their languages as descended from 'Hamitic'.
While calling Egyptians "Hamitic" isn't maybe terminology that would have been used in Medieval Europe (or maybe it was, I have no idea one way or the other on this), the sons of Ham in Genesis are "Cush, Mizraim, Phut, and Canaan" which were the names generally used in Hebrew for Kush, Egypt, Aksum/Ethiopia, and Canaan respectively.
The passage ends (after some stuff about the descendants of each of the sons) with "These are the sons of Ham by their clans and languages, in their territories and nations." (by the New International Version, wording may vary).
So the old testament does pretty directly say that Egypt and the Egyptian languages are descended from Ham. However, as you say @OneShot that doesn't make Hamitic "the language of Africa", neither Ancient Magic (as far as I'm aware) nor the bible claim that - under the umbrella of "languages of people descended from Ham" you have Egyptian languages, Cushite languages, Ethiopian, but also the language of the Philistines, Sumerian and Akkadian (through Nimrod, grandson of Ham), Hittite, Phoenician (and by extension, Punic) and more.
There is a lot of modern day "scholars" who put that interpretation on it, but the actual verse do not support that understanding- Genesis 10:10-12
And the beginning of his kingdom was Babel, and Erech, and Accad, and Calneh, in the land of Shinar.
11Out of that land went forth Asshur, and builded Nineveh, and the city Rehoboth, and Calah,
12And Resen between Nineveh and Calah: the same is a great city.
Which are all areas of the middle east, not Africa. It continues on from there, but the regions settled by Ham and his descendants are explicitly middle eastern, not something than needs to be inferred to be Egypt or Africa.
In fact, checking further, Honorius Augustodunensis wrote in 1100 AD that the serfs of Europe were the descendants of Ham, and thus their subjugation was justified, so under a philosophy following Medieval thought, the descendants of Ham would have been in Europe, not Africa.
Actually, reading the Old Testament, in Hebrew, @Argentius is correct. Genesys 10:6 lists the children of Ham, and 10-12 actually refers to the children of Nimrod, one of Ham's children.
I should have kept apart the descendents of Ham and of Canaan here. The biblical "Curse of Ham" by Noah - used over the centuries as a base for all kinds of racist arguments - targets actually only Canaan, Ham's fourth son.
Reading it again, it does indeed only settle on Canaan, and his descendants.
But, that said, amongst Ham's children are the egyptians, ethiopians, and others, who are native to Africa. So calling Hamitic a language of Africa is incorrect in historical sight, but might not be in how Europe sees it. Plus, the fertile crescent in Asia has also seen invaders from the arab peninsula, and persia, and other places further away.
Interestingly the groups singled out as being the descendants of Ham here, seem to conform quite well to the groups who speak languages of the Afro-Asiatic language family. A family that includes Ancient egyptian and its modern descendant Coptic, as well as most the modern Ethiopian languages (and on its other branch the semitic languages). The Kushitic language has unknown ancestry but may also be Afro-Asiatic.