I'm interpreting "science major" as having all the prereqs out of the way. I'm also interpreting your usage of direct linkage to mean that there's no glide year and there's some sort of guarantee.
As far as linkage goes, there are very few programs with such an offer. I can tell you that Wake Forest has a postbac program w/ a linkage (there's very few spots, it's meant for underrepresented students, and it's very competitive to get into) and UConn has a postbac that offers 1/3 of its postbac students a contingency acceptance (again, very few spots and from what I've been told, it's hard to get into if you're not a resident).
Wake Forest
UConn
I just found another one today...Duquesne Univerity has a direct linkage (I don't know the details) in its Enhancement Track postbac to Lake Erie College of Osteopathic Medicine (I'm guessing the one in Pennsylvania, not Florida, but I could be wrong).
Duquesne Postbac
LECOM linkage info at the bottom
Special masters programs/special premed grad programs, which are for those who have completed the science prereqs, don't have an officially guaranteed, direct-linkage, but those who perform among the top tend to gain acceptances to the med schools. Many of these offer guaranteed interviews if you score a certain MCAT and a specified minimum gpa--but don't interpret this as a guaranteed acceptance.
Hope that helps a little
Phil
😀
