Accelerating Forest Restoration Act of 2019 This bill authorizes the Department of Agriculture (USDA) to designate a forest restoration byproduct as a low-value or no-value restoration byproduct if it was harvested in accordance with the requirements of the Collaborative Forest Landscape Restoration Program and is within any geographic area of the Four Forests Restoration Initiative. USDA must permit unprocessed forest restoration byproducts and low-value and no-value restoration byproducts to be exported from the United States. Furthermore, USDA must exclude low-value or no-value restoration byproducts from the requirement to paint, brand, or hammerstamp timber. The bill also sets forth provisions regarding certain vehicles and equipment used in projects under the restoration program.