Before playing the NHL, Fleischmann played 2 seasons with Moose Jaw Warriors of the Western Hockey League. He was drafted by the Detroit Red Wings with the 63rd overall pick in the 2002 NHL Entry Draft. He never played with the Red Wings however and he along with draft picks were traded to the Washington Capitals for Robert Lang. He played 3 seasons in the AHL with their affiliate, the Hershey Bears. Fleischmann would play 6 seasons with the Capitals and was traded to the Colorado Avalanche for Scott Hannan on November 30, 2010. His season with the Avalanche was cut short when he was diagnosed with pulmonary emboli and had to miss the rest of the season.