CRP Grazing Flexibility Act This bill amends the Food Security Act of 1985 to allow grazing to be used as a mid-contract management practice under the Conservation Reserve Program (CRP) without any reduction in the rental rate if the grazing is consistent with the conservation of soil, water, and wildlife habitat. The Department of Agriculture may not make cost sharing payments for grazing undertaken pursuant to this bill. (CRP provides payments to farmers who agree to remove environmentally sensitive land from agricultural production and plant species that will improve environmental health and quality. Farmers with certain CRP contracts are required to apply authorized mid-contract management practices to CRP land to implement the conservation plan.)