I've been searching for this surname for a while and finally found the variant Kinnebrew on ancestry's last name origin site, which describes it as: "Americanized form of Scottish Kinniburgh, from the female personal name Kynborough, a survival of Old English female personal name Cyneburh. Compare English Kimbrough".
I'm far from being an expert but it seems very strange to me that a Scottish surname should be derived from an Old English, and female, name. If this was true I though that it would ultimately be derived from a place name as apparently Kimberley in Norfolk is of the 'Cyneburh' derivation, but I can't find Kinniburgh, or anything near, as a place name.
An expert opinion on whether you think this is correct would be appreciated!