Burns entered his freshman season at Tennessee as a member of the Volunteers' starting rotation.[3][4] He finished the season with a 8-2 record and 2.91 ERA with 103 strikeouts in 81+1⁄3 innings pitched. Burns was named the Freshman Pitcher of the Year by the National Collegiate Baseball Writers Association at the end of the season.[5]
Burns entered his sophomore season as a member of the Volunteers' starting rotation, but was moved to a relief role midway through the season after going 2-3 with a 6.10 ERA as starter.[6] In postseason play, Burns allowed only one run scored and struck out 22 over 16 innings pitched, including throwing six scoreless innings with nine strikeouts in a 6-4 win over Stanford in the 2023 Men's College World Series.[7] He finished the season with a 5-3 record and two saves with a 4.25 ERA and 114 strikeouts over 72 innings pitched. After the season, Burns entered the NCAA transfer portal.[8]
The Cincinnati Reds selected Burns in the first round of the 2024 Major League Baseball draft with the second overall pick. On July 18, he signed with the team for $9.25 million, breaking the MLB signing bonus record set by Paul Skenes the year prior.[10]