During the late 1950s and early 1960s, the U.S. Navy and the U.S. Army had ground launched antiaircraft missiles with this design. One of them was named the Monark and another the Bomark. The Army's was launched from a trailer mounted launcher and the Navy's was launched from rails on some battleships and cruisers. They used JATO bottles for initial lift off and it's own internal jet engine after reaching a certain airspeed.
Since the clip is silver colored, it MIGHT be a tie tack purchased at a base clothing sales store on a Navy or Army base. I got a hat pin at Tinker AFB with the profile of an E-3 (my plane), but IT was made of a cheap gold toned pot metal. Older types of those tie pins were usually made from some decent materials.