I'm not the best at Chinese history post Qing Dynasty, but I do know China was riddled with civil war from 1912 when the Republic of China was founded all the way until the rise of Mao and a Communist China. But to my knowledge, between 1912 and 1931 when the Japanese first attacked, the Republic wasn't overthrown and replaced with a new Republic.
TLDR: actually the government was effectively overthrown twice during that time.
In short and simple terms, Sun Yat-sen believed that the five colors of the stripe representing five ethnic groups still implied a rank with the top-bottom arrangement, so he was against using this as the national flag all the time.
Now for the long story.
In 1912 when the national flag was first decided by the provisional parliament, Sun was not in office (Yuan Shi-kai was appointed the provisional president) so he had no final say in it, and the stripes were officially selected.
From 1912 to 1916, tensions rose between Yuan and Sun, and eventually the situation worsened so much for Sun's party that he decided to fled to Japan, from where he called for a second revolution to overthrow Yuan.
Then in 1914, Yuan dissolved the parliament and started his political maneuvers to eventually proclaim himself the Emperor of the Chinese Empire, i.e. a return to monarchy. The stripes were changed to a red cross with the remaining four colors on the four sides.
It was a short-lived monarchy as Yuan still didn't have effective control over the whole of China, and the provinces revolted one after another, with provincial armies marching on the capital in order to restore the republic.
The monarchy ended in less than 3 months, and China was again in a state of disarray. Regional warlords exercised effective control over their local provinces while still maintaining the internationally recognized ROC government facade.
It was at this time when Sun Yat-sen realized that he was never going to get anywhere without an actual army under his command, so he returned to the southern provinces where he was most influential, rebuilding his party, founding the Kuomingtang (KMT) under the blue sky white sun flag, and building the Whampoa military academy, making preparations to wipe out the warlords for good.
Between 1920 and 1925, the regional warlords themselves engaged in skirmishes and after a successful coup by one of the warlords, Sun was made president in 1921. He again tried to replace the stripe flag with the blue sky and white sun, but the previous government still had a firm hold over the country, and the stripe flag was still widely recognized.
So in 1924, the KMT unilaterally decided that they will use the blue sky and white sun as the flag of the ROC. While Sun died in 1925, his successor Chiang Kai-shek inherited his visions and in 1926, the KMT troops marched and the the Northern Expedition began.
As the KMT troops conquered/pacified each region, the blue sky white sun flag was flown and steadily gained recognition.
It took two years to pacify all the warlords, and with political control over the whole of China, the stripe flag was declared obsolete in 1928 and the blue sky white sun flag was named the new national flag.
Finally, in 1946, the flag was officially written into the constitution.