Before I start, I'm not saying Khan would definitely win, just that he's Mayweather most dangerous opponent. My money would still be on FMJ. In hindsight, that may be a doing Danny Garcia a little disservice, although I do think Khan's style is better suited to causing Mayweather trouble.
1) His speed, Mayweather relies on fighters coming at him and pressing, this allows him to fight off the back foot and pick opponents off. Because Khan's speed is his biggest asset, it enables him to duck in and out of range, landing punches in bunches and stepping out, you can't box off the back foot against someone like that, it removes one of Mayweathers biggest assets.
2) Khan's style allows him to nick rounds, the flurry of punches looks exciting, gives you opportunity to land and impresses judges. You do this a couple of times per round, against a defensive fighter, particularly towards the end, and you can steal rounds without working too hard - very important for someone that struggles with endurance.
3) Khan has Vegas clout. He may not be popular on these shores, but he is a big draw in the states. They like him there, he sells tickets there, and he is big in Vegas. This is massive when it comes to scorecards. We all know how the cards favour champions and home fighters, and this is never truer than with Mayweather. Khan's one of the few fighters who holds enough sway in Vegas to temper that favoritism, somewhat anyway, coupled with his style in the ring; he's far better suited to winning rounds than anyone else around, in my opinion.
It's funny you mention his chin, because whilst suspect, it's probably not his weakest attribute, that would be his arrogance fueled ill-discipline, which obviously exposes his chin. It's when he thinks he's a fighter, not a boxer, he takes risks and exposes himself and other weakness. The other aspect he'd need to work on, is his ability to last the distance, he's notoriously laborious in the latter rounds, he should of been counted out against Maidana when he wouldn't stand let alone fight (a fight that's lauded amongst his greatest achievements, oddly). This is natural for a fighter that uses speed and a large number of punches, but he needs to master that.
He does have a lot of chances, and I do dislike him immensely, he's won fights he shouldn't have (Maidana) and been embarrassed on a number of occasions; but he does have victories against Malignaggi, Barrera, Maidana (despite what I think about it), McCloskey and Judah. and his last victory against Alexander was very good. So he does deserve to be around the elite, even if he is a grade A nob.