Make an Appointment. + Locations, Office Hours & Directions. Brackett Rheumatology. 6145 Shallowford Road, Suite 102, Chattanooga, TN 37421 map. Call for an Appointment. Dr. Richard Brackett is a rheumatologist in Chattanooga, TN. He treats disorders affecting the joints, muscles and bones (and may also involve other organ systems)..