Burnham played college football for the Tulsa Golden Hurricane, the only NCAA Division I school that recruited him. After he developed a serious infection when he cut his arm in practice, he sat out his freshman year with redshirt status in 2008. He played as a defensive back in 2009 and 2010 before switching to the wide receiver position for his junior year. In his first year at that position, Burnham caught 54 receptions for 850 yards and a team-best nine touchdowns. Burnham was injured in the third quarter of the first game of the 2012 season against Iowa State. He suffered a tornACL injury which ended his final year of NCAA eligibility. Tulsa sought a waiver from the NCAA to allow Burnham to compete in his sixth-year given the early timing of his injury, but this request and its appeal were declined.
Professional career
Burnham was signed as a free agent by BC Lions in May 2014 for the upcoming season. Initially playing on the practice squad, he made his pro debut in Week 13 against the Toronto Argonauts, in which he caught five passes for 90 yards and a touchdown. His season was cut short one week later when he suffered a lacerated spleen. In his second season in the CFL Burnham played in 11 games catching 35 passes 423 yards with 2 touchdowns. Burnham had a breakout season in 2016, playing in all 18 games for the first time in his career he set personal bests in catches, yards and touchdowns. His 1,392 receiving yards was fourth highest in the league that year. Burnham was set to become a free agent in February 2017. On December 6, 2016, Burnham had a workout with the Minnesota Vikings, and a workout with the New York Jets on December 15, 2016. According to BC Lions head coachWally Buono, Burnham had workouts with somewhere between 10 and 12 NFL teams between the end of the 2016 season and January 31, 2017, at which time pending CFL free agents were no longer allowed to work out with NFL teams until their contracts expired on February 14, 2017. On February 10, 2017, Burnham and the Lions agreed to a two-year contract extension. Over the following two seasons Burnham continued to be a key part of the Lions passing attack, catching over 148 passes for 2,231 yards with 16 touchdowns. Identically to two years prior, on February, 10, 2019, Burnham and the Lions agreed to a two-year contract extension. He had a career-high 100 receptions for 1,492 receiving yards and 11 touchdowns en route to being named a CFL All-Star.