Physician Pro Bono Care Act of 2019 This bill allows a tax deduction for direct primary care physicians who provide charity care. The care must be provided without expectation of reimbursement and to an individual enrolled in Medicaid or the Children's Health Insurance Program (CHIP). A "direct primary care physician" is a physician who provides primary care (1) to individuals who have paid a periodic subscription fee, and (2) in exchange for a fee that is published on a publicly available website of the physician. The bill also specifies that a physician is not liable under federal or state law for harm caused by an act or omission of the physician, or attending medical personnel supporting the physician, if the act or omission (1) occurs in the course of furnishing charity care, and (2) was not grossly negligent. The bill preempts laws of a state or a political subdivision of the state that are inconsistent with this provision, unless the laws provide greater protection from liability for a defendant.