Farming Flexibility Act of 2013 - Amends the Food, Conservation, and Energy Act of 2008 to consider mung beans and pulse crops as covered commodities whose planting on base acres is prohibited unless the commodity, if planted, is destroyed before harvest.

Provides that: (1) as of crop year 2014 producers on a farm may reduce the base acres for any covered commodity for a crop year by one acre for each acre used for the production of fruits or vegetables (other than potatoes) for processing; (2) such acres devoted to fruits or vegetables shall be included in base acres for the covered commodity for the subsequent crop year unless the producers on the farm make the election to produce fruits and vegetables for the subsequent crop year; and (3) if a farm's base acres are recalculated the production of fruits or vegetables shall be considered to be the same as the planting, prevented planting, or production of a covered commodity.