I think these VIP flights are in Citations...not in "military transport" cargo planes.
I need to add to my previous post that the Citation jets are USMC & Army. Air Force flies the Gulfstream for VIPS. Accding to dh, all congresspersons must submit a request for transportation. It is not guaranteed that a request will be filled due to limits of a/c and pilot availability. Even the Commandant submits his request.