Animal Emergency Planning Act of 2014 - Amends the Animal Welfare Act to require research facilities, dealers, exhibitors, intermediate handlers, and carriers (covered persons) to develop, document, and follow a contingency plan to provide for the humane handling, treatment, transportation, housing, and care of their animals in the event of an emergency or disaster.

Requires the plan to:

• identify situations that the covered person might experience, including natural disasters and emergencies, that would trigger the need to implement the measures identified in the plan;
• outline tasks to be carried out in response to emergencies or disasters, including animal evacuation or shelter-in-place instructions and provisions for providing backup sources of food and water as well as sanitation, ventilation, bedding, and veterinary care;
• establish a chain of command and identify the individuals responsible for fulfilling the tasks; and
• address how response and recovery will be handled in terms of materials, resources, and training needed.

Requires covered persons to review their plan at least annually to ensure compliance with this Act, and train personnel in their roles and responsibilities as outlined in the plan, and promptly provide training when the plan changes.

Prohibits this Act from preempting state law that provides greater protection for animals.