Kennedy started playing junior hockey with the Winnipeg South Blues of the Manitoba Junior Hockey League (MJHL) in 1985. After being noticed by Graham James at a hockey camp, Kennedy joined the Swift Current Broncos of the Western Hockey League (WHL) for the 1986–87 season. Kennedy spent his entire WHL career with the Broncos, helping the team capture the 1989 Memorial Cup. For his play during the tournament, Kennedy was named to the Memorial Cup All-Star Team. He was also named to the WHL's Eastern Conference Second All-Star Team.