Gates probably at least 1000x-ed his parents wealth. By just about any measure that's being self-made, as the GGP correctly pointed out. If 1000x-ing doesn't count as self-made exactly what meaningful measure of self-madeness and social mobility do you propose?

   degree of privilege doesn't diminish 

Privilege is a vague term that has become a term of political abuse and has ceased to be analytically useful, I recommend to avoid it. For example, does anyone who uses it bother to quantify privilege, after all we all stand on the shoulders of giants? How is the modern use of the term privilege useful, given the vastly different outcomes of the children of the rich? As I said, not every child of upper middle class families become Gates/Zuck ... My inner Nietzsche smells ressentiment here.