Chances of partnership will be very small at all of those firms and in any case depend on so many factors (many of which will be out of your control).Out of Kirkland, Milbank, Vinson, and Slaughters, Weil
Which is considered the most prestigious have offers/ACs for all of them.
Which would offer the best training and chance to reach partnership.
I’d pick based on the practice areas you’re interested in. If private capital, K&E; pretty much everything else, Slaughters