About Rex A. Birkmire, MD. Rex A. Birkmire, MD is a psychiatrist who practices at Rex A. Birkmire, MD Practice located at 650 S Central Ave in Oviedo, FL 32765 (Seminole County). Dr. Rex A. Birkmire has 15+ years of experience in psychiatry. Education. Rex A. Birkmire, MD earned a degree of a Doctor of Medicine. Licenses and Affiliations.