In general, you should use kinetic friction when there is sliding between interfaces and static friction when there is no sliding. Although RWOS is a situation with motion, you should use static friction because there is no instantaneous relative motion between the point of contact of the ball or disk and the surface it's rolling on.
In today's rolling ball example, the ball initially translates faster than rolling RWOS will allow, so there is sliding, and hence kinetic friction should be used. Eventually it slows down enough that it rolls without slipping; after that time (which wasn't asked about in the problem), static friction should be used.