Protecting Children with Food Allergies Act This bill requires the food and nutrition programs of the Department of Agriculture (USDA), such as the National School Lunch Program, to include training requirements, training opportunities, and other educational resources that address food allergies. Specifically, USDA must develop and publish training modules and other educational materials for food service personnel in schools relating to (1) preventing allergic reactions to food, including making food substitutions available for children with food allergies; (2) identifying symptoms of such reactions; and (3) responding to the reactions. Further, the bill requires school food service personnel who participate in the National School Lunch Program and the School Breakfast Program to complete the training and certify their competence in preventing, identifying, and responding to food allergies. USDA must also make the training available to personnel under other child nutrition programs, including the Special Milk Program, the Summer Food Service Program, and the Child and Adult Care Food Program. Additionally, USDA must incorporate food allergy information into its nutrition education materials for participants under the Special Supplemental Nutrition Program for Women, Infants, and Children (WIC).