This is the flag of British Korea. It's from a world where it was Britain, rather than America, which convinced Japan to come out of isolation. The British had intended to add Japan to their empire, but it soon became clear this wouldn't be feasible. The British, however, had been poking around Korea, which presented a much easier target, and thus British Korea was born. Side effects of this included a Spanish-Japanese war in which Japan took the Philippines, Guam and the Marianas Islands; as well as Japanese participation in the Scramble for Africa.
British Korea was occupied by the Japanese during World War II, but the British regained it after the war. The Soviets demanded control of Northern Korea, but the British wished it to stay unified. As a compromise, British Korea remained unified while Japan was split into a Communist North and a Democratic South. Korea officially gained independence from the British in the 1970s.
Also, since I know someone will say it, British Korea is Best Korea.