The Kirklin Clinic of UAB Hospital (TKC) The Kirklin Clinic — First Floor 2000 6th Avenue South Birmingham, AL 35233 (205) 801-8415. Hours of Operation. Monday - Friday 8:30 A.M. - 5:00 P.M. Parking. Enter The Kirklin Clinic of UAB Hospital Parking Deck near the corner of Richard Arrington Jr. Blvd. and 6th Avenue South..