As a prolific scorer, Fleischmann experienced his first taste of professional hockey late in the 2002–03 season, appearing in eight games out on loan with third-division team HC Nový Jičín.

With aspirations for an NHL career, Fleischmann immediately made the transition to North America by joining the Moose Jaw Warriors of the Western Hockey League (WHL) for the 2002–03 season.

In the 2003–04 season, Fleischmann improved his offensive numbers with Moose Jaw to post 30 goals and 75 points in 60 games and earn selection to the WHL East Second All-Star Team.

During the campaign, on February 27, 2004, Fleischmann's NHL rights were traded with draft picks by the Red Wings to the Washington Capitals in exchange for fellow countryman Robert Lang.

[3] In his third game with the Capitals, he collected his first NHL point, an assist on a goal to Brian Willsie, in a 5–4 victory over the Toronto Maple Leafs on November 6.

[4] Despite a near month-long stay, he was returned to Hershey and under the tutelage of Head Coach Bruce Boudreau, progressed to lead the team with 30 goals in just 57 games.

In the Calder Cup playoffs, Fleischmann helped carry the Bears to the Championship, leading the League with 21 assists and the team with 32 points in 20 games.

[5] Fleischmann failed to make the Capitals' opening night roster out of training camp for the 2006–07 season and scored 51 points in only 45 games in spending the majority of the first half of the campaign with the Bears.

After returning to the Czech Republic in the off-season, Fleischmann was found to have developed a blood clot in his leg due to deep vein thrombosis from the cross-Atlantic flight and would miss the pre-season and the start of the 2009–10 season.

[20] Fleischmann's torrid start with the Avalanche, scoring 21 points in 22 games, came to a sudden halt on January 20, when it was revealed that he was diagnosed with pulmonary emboli and would miss the remainder of the 2010–11 season.

Fleischmann compiled 10 goals and 10 assists in 57 games with the Canadiens before he was traded to the Chicago Blackhawks along with teammate Dale Weise in exchange for a 2018 second-round draft pick and Phillip Danault.

[28] While with the Moose Jaw Warriors, Fleischmann earned consecutive selections in the Czech World Junior Championship squad's for 2003 and 2004 respective sixth and fourth-place finishes.