Burns was a four-year basketball captain for John Marshall High School in San Antonio, Texas. Entering his freshman season, he stood 5'7 and weighed 110 lbs. Burns earned All-District honors in each season. As a senior, he led his team to the Conference 6A Region IV playoffs for its first time in 20 years and was named to the All-Region team. After initially committing to NCAA Division II program Midwestern State, he switched his commitment to Colgate, his only NCAA Division I offer. To meet Colgate's academic requirements, Burns attended Kent School in Kent, Connecticut for a prep year. He averaged 19 points, five rebounds and four assists per game, leading Kent to the Founders League title while sharing league most valuable player honors.
College career
On November 19, 2017, in his third game for Colgate, Burns scored 26 points and shot 12-of-15 from the field in a 93–88 win over UMBC. He was subsequently named Patriot League Rookie of the Week. On January 27, he scored a freshman season-high 27 points in an 83–69 victory over American. Burns subsequently earned Patriot League Rookie of the Week honors for a third time. As a freshman, he averaged 11.9 points, 2.9 assists and 2.7 rebounds per game, making the Patriot League All-Rookie Team. In the second game as a sophomore, on November 9, 2018, Burns recorded 30 points, six assists and five rebounds in an 87–74 win over Monmouth. Four days later, he was named Patriot League Player of the Week. On March 13, 2019, Burns scored a sophomore season-high 35 points to go with six assists and three steals, leading his team to a 94–80 victory over Bucknell in the 2019 Patriot League Tournament final. He was named tournament MVP and helped Colgate earn its first NCAA Tournament berth since 1996. In the first round of the 2019 NCAA Tournament, Burns scored 32 points and made a career-high eight three-pointers in a 77–70 loss to second-seeded Tennessee. As a sophomore, he averaged 16.3 points, 5.7 assists and three rebounds per game and was named to the second team All-Patriot League. On November 26, 2019, in his junior season, Burns scored a career-high 40 points and made eight three-pointers in a 99–81 win over Green Bay at the Legends Classic and was named tournament MVP. He recorded the most single-game points by a Colgate player since Tucker Neale in 1995 and surpassed the tournament scoring record. The performance helped him win Patriot League Player of the Week and Lou Henson National Player of the Week recognition on December 2. Burns recorded 21 points and 10 assists in a December 22 victory over Columbia, 89–71, before being named Patriot League Player of the Week again. As a junior, he averaged 15.8 points, 4.5 assists, 3.2 rebounds and 1.7 steals per game, earning first-team All-Patriot League honors. Following the season he declared for the 2020 NBA draft.
