Mariánské Lázně
Vlček was born in Mariánské Lázně. A defender, he played youth football for Lokomotiva Mariánské Lázně and Škoda Plzeň. He then played for Sokol Svéradice and VTJ Karlovy Vary until returning to his former team Škoda Plzeň, then FC Viktoria Plzeň, where he played for four more seasons. During the 1996–97 season, Vlček transferred to Slavia Prague, where he would spend a further four seasons.