I play assault and I drop the Medikit liberally. Unfortunately, I've never seen the exp bar increase. There even appears to be a service star icon next to the kit on the equipment selection screen... how would one go about obtaining it?
It seems like it's bugged (or unimplemented). Others are reporting the same thing. If you're throwing out medkits and getting points for healing your teammates, and it's still not moving, it might not be enabled.