His first club was FC Vekta. Kunchev made his debut in professional football as a 17-year-old for
Lokomotiv Plovdiv. He signed with
Levski Sofia in 2014, but was released after making only a few appearances for the team following a goalkeeping mistake made in a match against
Beroe. He subsequently relocated to
Greece. Kunchev played for
Lokomotiv Gorna Oryahovitsa one season but left the club in June 2017. On 11 August 2017, he joined
Vihren Sandanski. ==International career==