Fire Fighters and EMS Employer-Employee Cooperation Act This bill requires the Federal Labor Relations Authority to determine whether a state substantially provides fire and emergency medical services (EMS) personnel the right to form and join a labor organization; recognition by fire and EMS employers of the employees' labor organization, agreement to bargain with the organization, and reduction of any agreements to writing in a contract or memorandum of understanding; the right to bargain over hours, wages, and terms and conditions of employment; and arbitration or other mechanisms to resolve an impasse in collective bargaining negotiations. The bill makes the authority responsible for (1) determining the appropriateness of units for labor representation; (2) supervising elections; (3) conducting hearings and resolving complaints of unfair labor practices; and (4) protecting the right of employees to form, join, or assist any labor organization, or to refrain from doing so. An employer, fire and EMS personnel, or labor organization may not engage in a lockout, sickout, work slowdown, strike, or any other organized job action that will measurably disrupt the delivery of emergency services and is designed to compel an employer, fire and EMS personnel, or labor organization to agree to the terms of a proposed contract.