Kelly played two years at Owens Community College, where he averaged 17.9 points, 10 rebounds, 1 assist, 1.5 steals and 1.5 blocks per game, becoming the first player in program history to record 1,000 points, 600 rebounds, 100 steals and 100 blocks in his career. Kelly was named First Team All-Ohio Community College Athletic Conference, First Team All-Region XII and NJCAA D-II Second Team All-American as a sophomore. His time at Owens resulted in a National Top 100 Junior College Ranking and he was considered one of the top Junior College recruits in the country for the 2013 class. In his junior year, Kelly played at University of Miami, after deciding between Michigan State, West Virginia, and New Mexico. He went on to average 6.0 points, 3.7 rebounds in 17.9 minutes, shooting 40.5 percent from 3-point range. On May 16, 2014, Kelly was transferred from Miami to Marshall, but sat out first season at Marshall per NCAA Transfer rules. In his senior year at Marshall, Kelly led the team in scoring, rebounding, steals and blocks, becoming one of two players in Herd history to record at least 600 points and 300 rebounds in a single season. Kelly was named three-time Conference USA Player of the Week, C-USA Newcomer of the Year and First-team All-C-USA.
On November 7, 2017, Kelly signed a one-year deal with the Changwon LG Sakers. On December 7, 2017, Kelly recorded a double-double with a career-high 46 points and 12 rebounds, shooting 21-of-30 from the field, in a 93–94 loss to Anyang KGC. In 45 games played for the Sakers, Kelly finished as the KBL third-leading rebounder with 11 per game, and also averaged 21.3 points, 1.4 assists and 1 steal per game.
On July 9, 2018, Kelly signed with the French team Levallois Metropolitans. However, one month later, he parted ways with Levallois before appearing in a game for them. On September 3, 2018, Kelly signed with the Israeli team Hapoel Gilboa Galil for the 2018–19 season. On February 4, 2019, Kelly recorded 26 points, shooting 12-for-16 from the field, along with six rebounds, four assists and three blocks, leading Gilboa Galil to an 89–87 win over Ironi Nahariya. He was subsequently named Israeli League Round 17 MVP. In 33 games played for Gilboa Galil, he averaged 15.1 points, 7.9 rebounds, 1.7 assists and 1.1 steals per game, while shooting.578 from the floor.
On November 19, 2019, Kelly signed a one-month deal with Maccabi Rishon LeZion as an injury cover for Darryl Monroe. On December 18, 2019, Kelly recorded a season-high 27 points, while shooting 12-of-17 from the field, along with 12 rebounds, four assists and four steals for 40 PIR in a 96–92 overtime win over ratiopharm Ulm. He was named the EuroCup Round 10 MVP.
