As far as I know, they have to have CPLs and command instrument ratings under the civvy regs, and use (or have previously used) some civil check and training pilots to carry out endorsements and checks, as well as in-house check and training.
That applies for all civil-registered machines that are used by the military, such as the King Airs (and 1900s now I think) used by 32 SQN for Nav training at Sale.
For machines that are on the military register, they don't need civil licenses or ratings, but use the usual military training and checking systems.
As an aside, a military pilot who has passed a post-wings operational conversion course becomes eligible for issue of a CPL (A or H as applicable) on application. Instrument and instructor ratings don't carry over in the same way, although there are significant exemptions re courses of training.