Jiang Kun started his professional football career in 1997 with Bayi Football Team after graduating from their youth team. He would gradually establish himself as a regular within the team and help them receive promotion to the top tier in the 2000 league season. At the end of the 2003 league season Bayi Football Team disbanded and Jiang Kun was free to transfer to any other club.
Jiang Kun would decide to join another top tier club Sichuan Guancheng at the beginning of 2004 Chinese Super League season. He would have a solid start to his Sichuan career when he was immediately named as a first choice regular and would even score his first goal by the third league game against Shanghai Shenhua on May 26, 2004 in 1-1 draw. Results were not kind to Sichuan and he found himself increasingly dropped from the team and by the end of the season he would only play in ten league games.
Shanghai
In the 2005 league season he moved to the newly promoted second tier club Shanghai Jiucheng and would make his competitive debut in a league game on March 4, 2005 against Nanjing Yoyo in a 1-1 draw. This was followed by his first goal for the club against Yanbian FC in a league game on March 19, 2005 that Shanghai Jiucheng won 2-0. By the end of the season Jiang had established himself as a vital member of the team by playing in 23 games and scoring 6 goals. Off the field the club's owner Zhu Jun acquired top tier club Shanghai United F.C. and hoped to merge both the two teams, however this wasn't possible due to the transfer rules in Chinese football. Instead Jiang along with four other players joined Shanghai United F.C. while Shanghai Jiucheng was sold off to a new owner. In the 2007 season Shanghai United F.C. was dissolved to allow them to join neighbouring Super League team Shanghai Shenhua, allowing both teams to merge. All the players from Shanghai United F.C. would move to Shanghai Shenhua and despite the inflamed squad Jiang Kun was one of the few consistent first choice players within the team. This continued the following season, however despite the significantly reduced squad by the beginning of the 2009 league season he was loaned out to Henan Construction. He played 27 league games and scored 1 goal in Season 2009.
Jiang was called up to the Chinese senior national team where he made his debut on June 7, 2006 in a friendly against France in a 3-1 defeat coming on as a late substitute for Zhao Junzhe. In preparation for the 2007 AFC Asian Cup he would make several further friendly appearances, however the Chinese Head coachZhu Guanghu decided that his performances were not good enough to be included in the squad to go to the tournament.