What is the measurable genetic variance between a human and a chimpanzee?

Weird question. Humans and chimpanzees are about 98.8% similar.

And how many fixed mutations are required to bridge that gap?

"Fixed mutations" is not a scientific term, and obviously sex casues more genetic changes than mutation. Given that humans and chimpanzees are cousins - neither is the ancestor of the other - we've seen a very predictable amount of genetic drift in the seven million years since humans and chimpanzees shared a common ancestor.