What does the American Flag symbolize for the US?

There is no such thing as the 'American flag'.

Many people, incorrectly, call the US flag the American flag. This is obviously incorrect. There are many other countries in America with their own flag.

As with any flag it is a symbol of nationalism. A 'tribe' or society on which values are built and held.

Those values may vary within that society but there is usually an overall sense of identity and purpose.