Federal Employee Accountability Act of 2013 - Repeals provisions: (1) authorizing a federal employee representing an exclusive representative in the negotiation of a collective bargaining agreement official time for such purpose during the time such employee otherwise would be in a duty status; and (2) requiring the Federal Labor Relations Authority (FLRA) to determine whether any employee participating for, or on behalf of, a labor organization in any phase of proceedings before it shall be authorized official time for that purpose.