Amick began racing in jalopies in the Northwestern United States before switching to midget car racing.[2] He competed in USAC National midgets for three seasons, finishing in the top ten points each season, and won 16 feature races.[2] He totaled 38 wins including the 1957 Turkey Night Grand Prix.[2]
He moved to Indy cars and won three times in 43 starts.[2] In his rookie appearance at the Indianapolis 500 in 1958, Amick was assigned a "lay-down" roadster commissioned by car owner Norm Demler, designed by Quinn Epperly, and built by master Indianapolis chief mechanic George Salih. Amick found himself running a comfortable second to leader Jimmy Bryan with just 20 laps remaining. Demler and Salih felt Amick was in a position to catch Bryan and perhaps even win, but decided against pushing their rookie driver into a potentially fatal mistake, and Amick came home an easy second. He was named the 1958 Indianapolis 500 Rookie of the Year.[3]