Kukleta started to play his club football in Czechoslovakia for Zbrojovka Brno and RH Cheb.
[3] In 1991 Kukleta moved to Spain to play for Real Betis, where he joined compatriot manager Jozef Jarabinský, as well as players Michal Bílek and Alois Grussmann.
[2] Kukleta went on to play in the lower leagues for Děčín, Zeman Brno, Mutěnice and Velké Meziříčí.
[1] Having scored on his only appearance for the Czechoslovakia Olympic team in 1987,[2] Kukleta made his debut for the full national side in January 1991 in a friendly match against Australia.
His only competitive appearance was in a 2–0 UEFA Euro 1992 qualifying win against Albania, where he played alongside Pavel Kuka.