In the US the flag is important, because of it's history and meaning. Many countries inherited their flags ... usually from controlling regimes many centuries ago, but ours we took time to look at it, time to design it to show exactly what our country stands for. Each color, the stripes, and the stars mean something to us. It's not just a symbol of our country, but a symbol of what our country stands and exists for.
the history of the design of the stars and stripes is very similar to the stories of other flag designs, and as you said most of the time flags are adaptations of previously used ones.
case in point:
no american exceptionalism.
Notice I said "many", not all. I was just explaining why the flag is so important to people in our country, not trying to belittle others.
USFlag.org: A website dedicated to the Flag of the United States of America - What do the colors of the Flag mean?
"The colors of the pales (the vertical stripes) are those used in the flag of the United States of America; White signifies purity and innocence, Red, hardiness & valour, and Blue, the color of the Chief (the broad band above the stripes) signifies vigilance, perseverance & justice."
The meanings to these colors were defined when the seal for congress was created, but:
"The star is a symbol of the heavens and the divine goal to which man has aspired from time immemorial; the stripe is symbolic of the rays of light emanating from the sun."
History of American Flag | USA Flag Site
In school we get a very watered down version of this (well did when I was in school) ... but this is the summary:
"Today the flag consists of thirteen horizontal stripes, seven red alternating with 6 white. The stripes represent the original 13 colonies, the stars represent the 50 states of the Union. The colors of the flag are symbolic as well: Red symbolizes Hardiness and Valor, White symbolizes Purity and Innocence and Blue represents Vigilance, Perseverance and Justice."
After all it's changes. Our country started with nothing but the flag, it is the very first piece of our history, we are a very young country after all. Everything prior to the flag's history was actually part of England's history, not ours.