Does the US military use metric system?
As the US military primarily flies and trains in US airspace, they use the standard measures associated with the airspace. That is feet (or flight levels), nautical miles and knots, inHg, and °F. Though, using °C is fairly common in the US now since weather reports shifted to the ICAO format. 

That said, the cockpit systems can be switched to HPa and meters for altitude and °C for temp for when they fly in airspace where that is the standard. Speed and distance are always in nm and kts.