Main Street Duncan, SC 29334. AFC Urgent Care in Duncan is open Monday through Friday from 8am to 8pm and Saturday through Sunday from 8am to 5pm. At AFC Urgent Care, we accept most major health insurance plans as well as honor Tricare and our Military. If you are looking for an urgent care near me for your family’s medical and healthcare needs, AFC Urgent Care and Walk-in clinic in Duncan, SC is an excellent resource for your needs. We treat children, adults and even senior patients 7 days a week. When you walk into AFC Urgent Care Duncan, you will be greeted by a friendly and experienced medical team. At our urgent care clinic, we focus on the patient. From a timely visit with a physician, to excellent medical treatment, AFC Urgent Care Duncan wants you and your loved ones to have the best experience possible at our clinic.