Interesting history regarding the flag.

China, contrary to what the Chinese Communist Party attempts to promote, is actually a multi-racial nation. Hence the very first flag used to represent the revolutionists in 1906 is actually the five-stripe flag.svg), showing red, yellow, blue, white and black to represent the five major ethnic groups in China. This flag was then adopted by the newly founded Republic of China in 1912 when the Qing Dynasty fell.

However, the leader of the revolutionists, Sun Yat-sen, later regarded the father of modern China, was against the use of the five-strip flag. He cited the fact that it was the same as the flag for Qing's top ranking officials, that the colors don't necessarily represent the five ethnic groups correctly, and that the vertical order still conveyed a notion of caste that is contrary to the ideal of equal value for the new nation.

Hence in 1921, when Sun was named president, he ordered to change the flag to the white-blue-red one posted by the op. However, it wasn't used in all of China, as China was essentially fighting a civil war with warlords from each region all using their own flags (some even minted their own coin).

It wasn't until 1928 when Sun's faction unified China (i.e. the end of the Northern Expedition, as Sun's faction was based in southern China) that this flag flew all over China.

And it took until 1946 when the constitution of the ROC was finalized that the status of this flag as the national flag was formalized in law.