Blue Water Navy Vietnam Veterans Act of 2019 This bill extends the presumption of service-connection for certain diseases associated with herbicide (e.g., Agent Orange) exposure to veterans who served (1) offshore of Vietnam between January 9, 1962, and May 7, 1975, or (2) in or near the Korean Demilitarized Zone between September 1, 1967, and August 31, 1971. Under a presumption of service-connection, specific disabilities or diseases diagnosed in certain veterans are presumed to have been caused by the circumstances of their military service. Health care benefits and disability compensation may then be awarded. The bill extends eligibility for health care, vocational training and rehabilitation, and monetary allowance to children with spina bifida who have at least one veteran parent who may have been exposed to an herbicide agent while serving in Thailand between January 9, 1962, and May 7, 1975. The Department of Veterans Affairs must report on the Follow-up Study of a National Cohort of Gulf War and Gulf War Era Veterans.