Bezos obviously knows how to run a company, but the only "brand" he has is (I think unfairly) "exploitative capitalism". If Bloomberg can't be president Bezos probably can't either. And probably wouldn't want to, to be honest.
Zuckerberg might want to, but he's universally despised on both sides of American politics, so no chance there.
(Not to mention that VP picks are normally used to broaden the ticket's appeal, not double down on it...)
I don't really see "exploitative capitalism" as being a problem for Bezos. As our current president has pointed out, it's just smart business. In our current political climate that will probably be lapped up by someone.
Running mate Zuckerberg?