The man who acted as Jesus does look like a Middle Eastern/Persian man. By the time Jesus was alive, Egypt was pretty much populated by Greek and Arabic looking people. Hell, the Romans were there too. Cleopatra (decendant of Alexander the Great) was alive about a 70 years before Jesus, give or take a few years.
So yes, Jesus\'s family could easily flee to Egypt without looking out of place.
However, I don\'t think Jesus was black. He defintiely wasn\'t white.