KAMPALA, Uganda—Ugandan presidential challenger Bobi Wine on Monday launched a court case seeking to overturn the reelection of President Yoweri Museveni, who has been in power for 35 years. Wine, whose real name is Kyagulanyi Ssentamu, had suggested he did not want to legitimize Museveni’s victory in last month’s polls by seeking justice with a court that has been reluctant to rule against the president in past elections. The Supreme Court ruled three times that electoral irregularities were not substantial enough to affect the outcome. Museveni won the Jan. 14 elections with 58 percent of the vote while Wine had 35 percent, according to final results announced last week by the electoral commission after accounting for results from nearly all polling stations. Wine has accused electoral authorities of declaring “cooked-up results,” alleging irregularities such as soldiers stuffing ballot boxes, casting ballots for people, and chasing voters away from polling stations …