2002-03: Burki played for the Winnipeg Warriors midget AAA where he finished among the league leaders in scoring with 77 points (37 goals, 40 assists). He was then drafted in the first round (17th overall) by the Wheat Kings in the 2002 WHL Bantam Draft. He played in two games after being drafted, seeing limited ice time.
2003-04: Burki continued to see more limited ice time during his first full season with the Wheat Kings. In 53 games, Burki finished second on the team in rookie scoring with 12 points (one goal, 11 assists). He was named to Team Western for the 2003 World U-17 Challenge held in Newfoundland.
2004-05: Burki continued to emerge as a player in his second full season with the Wheat Kings by nearly doubling his point total from the prior season. He finished the year with 23 points (10 goals, 13 assists) in 68 games. He also recorded 48 PIM. Burki helped the Wheat Kings go on to win the Eastern Conference Championship by recording 11 points (6 goals, 5 assists) in 24 games.
2005-06: Burki had his coming out party, leading the Wheat Kings in assists (34), points (61) and PPG (.87), his 27 goals were second best on the team. He finished in the top 25 in the WHL in points. His breakout season and very good draft workouts helped raise his NHL draft stock as he was rated as the 18th best North American Skater by the CSS.
2006-07: This marked the center’s final season with the Brandon Wheat Kings (WHL), and it was the best of his four year career in the league. In 70 games, he scored a career-high 36 goals and 85 points, while racking up 83 minutes in penalties, another career-high for Burki.
2007-08: His first year pro, Burki potted a pair of goals and nine points in 40 games with the Lake Erie Monsters (AHL). He also saw some action with the Johnstown Chiefs (ECHL), netting three goals and eight points through 12 games.2009-10: Assigned to ECHL affiliate Charlotte Checkers.
2008-09: Burki’s 2008-09 season mirrored his pervious one, seeing the center play the majority of his hockey with the Lake Erie Monsters (AHL). In 54 games he tallied a personal best nine goals and 19 points, while adding five more points (1g+4a) in 14 games with Johnstown (ECHL).