He was born in Lublin. He won the gold medal in the Flyweight class at the 1953 European Amateur Boxing Championships in Warsaw, and the bronze medal at the 1955 European Amateur Boxing Championships in West Berlin. Kukier was a Polish champion six times (1953–1957 and 1960). He competed thrice in the Boxing at the Summer Olympics (1952, 1956, 1960). Between 1951 and 1960 he was on the Polish national team and fought 35 times, winning 25 bouts and losing 10.