I'm not aware of an American Airlines store, but I do know about these:

DFW Employee Store: http://thedfwemployeestore.com
In Terminal C at the northern end by Gate C-2 as well as online. Tee shirts, patches, lanyards, apparel, luggage, caps, key chains, shoes, etc. Open to the public, near as I can recall normal USA work hours.

You can see some US Airways items here: http://www.airlineemployeeshop.com/category_s/2098.htm

US Airways aircraft models (Inc. DC-9): http://www.airlineemployeeshop.com/U...y_p/rt2694.htm

C. R. Smith Museum store: http://store.crsmithmuseum.org/store/
At C. R. Smith Museum, south end DFW near Flight Academy, etc. Museum includes airline memorabilia mostly from AA, now some US, including fully restored, fly able DC-3 Flagship Knoxville.

Gift shop offers range of items from models to cups, patches, etc. including Child Aviation Safety Restraint System (CARES) certified by the Federal Aviation Administration (FAA) for use on flights within the continental United States.