The two first tricolors where the flags of the Netherlands and that of France. The Dutch flag came from the colors of William of Orange used in the Dutch War of Independence against Spain, thus establishing the Dutch Republic. The French flag came from inserting the white of the French monarchy between the blue and red of Paris during the French Revolution.

Both of these flags represented countries at a point when they rejected monarchy and adopted republican ideals of government. During the mid-19th century, the symbolism of nationhood became very important to ethno-nationalist groups around the world, and nationalist republicans from Mexico to Ireland to Germany turned to the symbolism of France and the Netherlands in constructing their own national identity separate from the empires that had dominated the political landscape before that point. The flags of Italy, Ireland, Romania and Mexico are all explicitly based off the French tricolor, substituting a locally significant color scheme.

Subsequent movements in Africa would add to this general idea of basing flags of other symbolic countries. The Ethiopian flag, adopted in 1914, is a red, gold and green tricolor. Because Ethiopia was the only African nation to resist European colonialism, it became a symbol for independent Africa, with many African countries, such as Ghana, Mali and Cameroon, adopting the same color scheme.

This may be worth cross-posting to the vexillology subreddit.