Training the Next Generation of Primary Care Doctors Act of 2019 This bill alters funding provisions, and establishes additional reporting requirements, relating to the Teaching Health Center Graduate Medical Education Program, which is administered by the Health Resources and Services Administration (HRSA). The program supports training for primary-care-physician and dental residents at community-based clinics. The bill (1) establishes certain parameters for payments to approved and newly approved graduate medical-residency training programs, and (2) requires HRSA to publish a report regarding new and expanded programs.