To be honest I don't know how I'm not overstimulated and how my eyes don't physically hurt. Surely, OP knows something about color theory. I believe it's because the hues blend with each other, they use black to compensate for the eye-hurting brightness, and they use white to seperate the part where the colours clash, which is a genius idea most artists and designers I personally know don't think about. When creative brodies use a palette, they usually pick colours related to each other, which have a moderate to high amount of desaturation. Exceptions that look good aren't very easy to execute.
For example, here's Mayia the spring nation, also known as Mariposa. This countryhuman is mostly in desatured colours, except her little rainbow accessory. I think the bright colours work here because they don't take much space: the colours are balanced.
In a nutshell, I think the balance between black and white, desatured colours, and the bright colours are the reason this flag goes easy on my eyes.