On Independence Day we celebrate our founding as a nation - if we're going to have a flag-waving holiday, that's the logical choice. On Memorial Day we celebrate our fallen warriors - so that one makes sense, too. We have two days on which we celebrate specific American heroes - Presidents' Day and Martin Luther King Day - but those evince at most mild patriotic displays. Thanksgiving is traditionally American, but centers more around family than country. New Year's Day is a strictly secular, global holiday; finally, Easter and Christmas are religious, global holidays.
Other than minor holidays like Veteran's Day and Columbus Day, which most of us don't get anyway, that leaves only Labor Day. In my experience, Labor Day is third behind only Independence Day and Memorial Day in patriotic displays. In my town, for example, we have a fireworks display. I see kids wearing American flag clothing in the park.
But Labor Day is not especially American, and the part of it that is has not much to do with founding American values. Labor Day commemorates the bloody breaking of a strike in 1894. Its associations are with the International Labor movement and it is essentially the American version of May Day, which is the international (not American) socialist holiday (and also commemorates a massacre during a 19th-century strike). Labor Day was created as a conciliatory gesture toward the growing labor movement.
So I don't quite understand the fireworks and the flags. USA! USA! We're unionized!