There isn't an "academic physician" training program or residency per se.
Those interested in working as a physician at an academic medical center generally are advised to seek their residency training at such an institution and spend some years in the lab, doing research. You'll also find many in administrative positions (ie, department chairs) will also have some additional qualifications, ie, MBA, MPH, PhD, etc.
Obviously community residency programs also have academic physicians who also teach as part of their job requirement and it may not be necessary to do your residency at a university program. However, this is generally the route most suggest.
Hope this helps.