National Discovery Trails Act This bill amends the National Trails System Act to establish as part of the national trails system national discovery trails, which shall be extended, continuous interstate trails located to provide for outdoor recreation and travel and to connect representative examples of America's trails and communities. The bill authorizes the designation of such trails on federal lands and, with the owner's consent, on nonfederal lands. The 6,000-mile American Discovery Trail extending from Cape Henlopen State Park in Delaware to Point Reyes National Seashore in California, splitting into northern and southern routes at Cincinnati, Ohio, and rejoining at Denver, Colorado, is designated as a national discovery trail. The bill sets forth requirements for designation of a trail as a national discovery trail. The appropriate federal department for each national discovery trail shall: (1) administer the trail in cooperation with a competent trailwide volunteer-based organization; and (2) submit a comprehensive plan for the trail's protection, management, development, and use.