Kirkov was awarded a qualifying wildcard at the
2016 US Open having reached the final of the USTA National Boy's 18 Championships in Kalamazoo, Michigan. Kirkov made his Grand Slam doubles main draw debut at the
2017 US Open with
Danny Thomas after receiving a wildcard for winning the USTA Boy's 18 National hardcourt Championships in Kalamazoo with Thomas. In December 2019, Kirkov won the M15 in Cancun, Mexico, his first-ever
ITF World Tennis Tour title as the No. 4 seed defeating No. 3 seed
Nick Chappell in a close match with a scoreline of 6–7(3), 7–6(8), 7–6(1). He reached the third round at the
2023 US Open after receiving a wildcard partnering
Denis Kudla but lost to
Ivan Dodig and
Austin Krajicek. He entered the ATP 500
2024 Mubadala Citi DC Open in Washington as a lucky loser partnering
Evan King but they lost to
Lloyd Glasspool and
Santiago Gonzalez in the first round. He also received a wildcard in doubles for the
2024 US Open partnering
Christian Harrison. In March 2025, in Latin America, Kirkov won three back-to-back Challenger doubles titles in
Santiago,
Asunción, Paraguay and in
Concepción, Chile partnering again with Chilean Matias Soto. Following two challenger finals in Asia, Kirkov reached the top 100 in the doubles rankings on 5 May 2025 at world No. 98. He won his eight title at the
Challenger 100, the
2025 Wuxi Open, with
Bart Stevens. ==ATP Tour finals==