Farmers Feeding Families Act of 2022 This bill amends The Emergency Food Assistance Program (TEFAP) to authorize the Food and Nutrition Service (FNS) to provide funds for states to purchase priority agricultural products (e.g., fruits, vegetables, meats, and grains) from eligible small businesses and distribute them to needy persons through emergency feeding organizations. New farmers and small or mid-sized family farms qualify as eligible small businesses under this FNS program, as well as packers, distributors, cooperatives, and others that source agricultural products from them. The bill also requires a state's TEFAP plan eligibility standards to include, at a minimum, all individuals or households with an income less than 250% of the poverty line.