Elijah E. Cummings Federal Employee Antidiscrimination Act of 2019 This bill requires each federal agency to establish a model Equal Employment Opportunity Program that is independent of the agency's Human Capital or General Counsel office, and it establishes requirements related to complaints of discrimination and retaliation in the workplace. An agency must publish a notice of any final agency action or Equal Employment Opportunity Commission (EEOC) appellate decision involving a finding of prohibited discrimination or retaliation, and it must report certain data with respect to specified equal opportunity complaints. Each agency must establish a system to track complaints of discrimination and include a notation of any adverse action taken against an employee for discrimination or retaliation in the employee's personnel record. The EEOC must refer to the Office of Special Counsel a matter about which it issues an appellate decision involving a finding of discrimination or retaliation within a federal agency, and the Office of Special Counsel shall accept and review such referral for purposes of seeking disciplinary action. An employee who has authority to take, recommend, or approve any personnel action shall not implement or enforce a nondisclosure policy that prohibits or restricts an employee from disclosing information relating to (1) a violation of any law, rule, or regulation; (2) mismanagement, gross waste of funds, or abuse of authority; (3) a substantial and specific danger to public health or safety; or (4) any other whistle-blower protection.