Because I'm a nerd I'm gonna share the flag I designed for the United Republic of Nations in Legend of Korra.
So, it's divided into four quadrants, each representing one of the four nations. Going clockwise from the top left, it goes in the order of the Avatar Cycle. Red represents fire, white represents air, blue represents water, and green represents earth.
I chose white to represent air because choosing yellow (which the Air Nomads often wear) would make it look too much like the Windows logo, and I thought orange (the other color they often wear) was too similar to red and would be hard to distinguish. Also, white is the color of clouds, which, though made of water, float in the sky, which is the Air Nomads' domain. Sky bison are also an off-white color. :)
I also tried to keep air and water on the end away from the flagpole, as they are more fluid and should be flying free.
The symbol in the middle of it seems to be the seal of the United Republic, or some kind of symbol that represents it. It can be seen in pin form on the Council Member's clothes in season 1 (most often on Tenzin, who has the most screen time), and on President Raiko's lapel in seasons 2-4. I thought it would make the flag look more distinguished than just four squares sewn together.
The ratio is 2:3, which is a common ratio for flags in Asia (and actually the most common in the world).
If you would like to see what it looks like waving, feel free to click here!