And a note that says the Kitty Hawk can now fly this flag as she’s the oldest ship in the fleet. A google led me to this page with a ton of history on the Navy Jack. I highly recommend that you check it out.
Normally, only the oldest ship in the Navy flies the First Navy Jack. The Kitty Hawk became the oldest when the Independence was decommissioned in 1998. In 2002, however, all US ships were ordered to fly the First Navy Jack for the duration of the War on Terror.