Farmer Flexibility Act of 2014 - Amends the Agricultural Act of 2014 to require the Secretary of Agriculture (USDA) to extend the terms of marketing assistance loans in cases where a farmer has sold, transferred, or delivered the commodity subject to the loan to a purchaser who has filed for bankruptcy prior to payment. Provides that the extension shall last until after the bankruptcy case is closed or dismissed. Suspends the accrual of interest on the loan during the extension period.