Kibuuka studied at the Outward Bound School in Kenya. In 1968, he was one of the first blind people to ascend successfully to the peak of Mount Kilimanjaro, earning media attention as well as praise from the Ugandan Minister of Labour. Due to this event, he was invited to Norway by an "organisation promoting sports for the disabled". He arrived in Norway in 1972, a year after Idi Amin's rise to power in Uganda. Due to the situation in his country of origin, he was to remain in Norway permanently, but nonetheless competed for Uganda in the 1970s.
In the Men's short distance 10 km, he finished 16th, with a time of 58:24.
In the Men's middle distance 15 km, he finished 10th, with a time of 1:16:32.
He competed again in 1980, where he was once more the only African competitor. He entered two events:
In the Men's middle distance 10 km, he finished 12th, with a time of 49:52.
In the Men's long distance 20 km, he finished 11th, with a time of 1:42:17.
He did not compete again in the Winter Paralympics. Having obtained Norwegian citizenship, he began to compete for Norway at the Summer Paralympics.
Summer Paralympics
Despite having first moved to Norway due to his potential as a Winter Paralympian, and despite his solid performance for Uganda at the Winter Paralympics, it was as a runner that Kibuuka obtained all his Paralympic medals. At the 1984 Summer Paralympics in Stoke Mandeville and New York, representing Norway, he entered three events:
In the Men's 800 metres, he won his heat with a time of 2:07.83, and his semi-final in 2:12.13. Improving his time to 2:04.26, he finished second in the final, taking the silver medal behind Robert Matthews of Great Britain, who established a new world record in 2:02.33.
In the Men's 1500 metres, he finished first in his heat, and second in the final, taking a silver medal – again, behind a new world record by Matthews of Great Britain.
In the Men's 5000 metres, he took silver with a time of 16:42.18, behind Matthews' world record 16:36.90, and ahead of his Norwegian compatriot Joerund Gaasemyr, who took bronze in 17:55.73.
In the 1988 Games, he entered only the 1,500 and 5,000m events, winning bronze in the former, and silver in the latter. In 1992, he was Norway's flagbearer during the Games' opening ceremony. He entered the same events as in 1988, but finished fifth in the 1,500m and fourth in the 5,000m. While Matthews remained Paralympic champion, and Loevaas remained on the podium with bronze, Portugal's Paulo de Almeida Coelho finished second to edge Kibuuka off the podium. However, Kibuuka did also enter the marathonfor the first time, finishing in 2:51:34 to take silver, behind Italy's Carlo Durante. From then on, he would compete only in long distance running. In 1996, he entered the 10,000m as well as the marathon. He finished fourth in the former, in 36:10.58, and sixth in the latter, in 3:05:06. For his final appearance at the Paralympics, in 2000, he entered only the marathon, but injured himself during the race and failed to finish.