Bickmore is an unincorporated community and coal town in Clay County, West Virginia, United States. Bickmore is located on West Virginia R…Bickmore is an unincorporated community and coal town in Clay County, West Virginia, United States. Bickmore is located on West Virginia Route 16, 5.5 miles south-southwest of Clay. Bickmore has a post office with ZIP code 25019.