Hey medjuck, I'm programming some music for my new program, which debuts tomorrow on the eve of the 4th of July. It will include Duke Ellington's version of "Rhapsody in Blue" (a perennial Independence Day number for picnic-with-the-Pops affairs) and Charles Mingus' "Freedom" (not necessarily "patriotic," at least by the conservative definition of the word).
Off the top of my head:
Peggy Lee/Johnny Mercer, "Freedom Train"
Anything by Louis Armstrong (whose "symbolic" birthday remains July 4)
Paul Robeson, "Ballad for Americans" (not really jazz, but a 4th fave of mine)
Damn, there's much more, but I can't remember... I'll post whatever else I think of.