To file a complaint with American Airlines, contact Customer Relations either by mailing a letter to 4000 E. Sky Harbor Blvd. Phoenix, AZ 85034, or sending an email through its online form.
If the problem is specific to delayed baggage, call its customer service line at 800/371-4771 (4am–11pm PT, M–F). Whatever the issue, make sure you know your ticket number/record locator, mailing address, dates of travel, origin, and destination cities.