Fleßers first club was home town club 1. Football Club Viersen 05 before Borussia Mönchengladbach spotted and signed him. He joined Borussia Mönchengladbach"s senior team in 2005.
On 22 April 2006 he made his debut in the Bundesliga in the 2–2 draw with Hertha Bachelor of Science. On 2 May 2008, he announced his departure from Borussia Mönchengladbach and signed on 4 June 2008 a contract with 1.
FSV Mainz 05. After only one year with 1. FSV Mainz 05 he joined Football Club Ingolstadt 04.
After a half year in Ahlen, Fleßers joined Wuppertaler SV Borussia. He spent two years with Wuppertal, leaving in July 2013 after the club were relegated from the Regionalliga West, and signing for Rot-Weiß Oberhausen.
Fleßers has played in German national youth teams and the U21.