Traveling Parents Screening Consistency Act of 2019 This bill directs the Government Accountability Office (GAO) to review implementation of requirements regarding screening by the Transportation Security Administration (TSA) of baby formula, breast milk, purified deionized water for infants, and juice on airlines. The review shall include an assessment of whether the TSA effectively manages the consistency of the application of protocols to the screening of such products; the need for the TSA to update and revise procedures for screening such products; whether the TSA effectively tracks passenger complaints related to such screening to monitor trends and identify inconsistencies; the practices of the TSA with respect to communications and information sharing with passengers, air carriers, and airports relating to protocols for such screening; and the policies of the TSA regarding the screening of passengers with nursing products, including the extent to which such passengers are more likely to receive secondary screening. Additionally, the GAO must make recommendations for improving the practices of the TSA related to the screening of passengers with nursing products.