Federal Worker Childcare Protection Act of 2019 This bill provides for the reimbursement of childcare expenses of federal employees who are furloughed or working without pay during the lapse in appropriations that began on or about December 22, 2018. The reimbursements are provided (1) subject to appropriations, and (2) if the employee can provide documentation to the General Services Administration in the form of a receipt from a childcare provider.