skyward is correct
I had my private before UPT, after UPT I got my Comm-Multi Instrument Restricted to Centerline thrust due to having flown the T-38. When I went to do my CFI, I had to first get the Commercial Single Engine Add-on, then take the CFI rating. After flying C-130s, I got the centerline thrust restriction lifted from my multi.
Military Flight Instructors are generally good teachers, but AF AETC instructor training doesn't really do a good job of teaching FARs, airspace, uncontrolled airport ops (changing with the T-6 JPATS). It doesn't really cover the Fundamentals of Instructing very well either.
T-34 Navy and T-6 Air Force guys are probably the closest right now to being ready to take the CFI exam, but there is still a lot of civilian stuff to know. Guys who become MWS instructors in big planes without having ever taught in little planes are probably no where near ready to teach multi stuff in a Seminole/Duchess type aircraft. But I'd be willing to bet they could learn pretty fast.
If I were King of the FAA/Military/AOPA liason program, I would submit a proposal that all military flight instructors who are willing to go out and earn their initial CFI single engine, could then have their tickets stamped for whatever they are doing. I.E. guys at Primary Training bases could easily have their Instrument Instructor ratings and if they were instructing Multi such as T-1/T-44/T-38/T-37, they could have their multi engine add on as well. Maybe the guys who are instructing in Multi Center thrust airplanes would have to take a checkride in a non center thrust airplane. Who knows, will it ever happen--probably not.
