Dignity for Incarcerated Women Act of 2019 or the Dignity Act This bill establishes requirements for the treatment of prisoners. The Bureau of Prisons (BOP) must provide adequate health care, provide videoconferencing free of charge, train employees to identify trauma-related health needs, and make specified health products (e.g., tampons) available free of charge. Additionally, with respect to prisoners who are primary caretaker parents, the BOP must provide parenting classes, allow visitation from family members, and establish a pilot program to allow overnight visits from family members. Finally, the bill allows a prisoner who is pregnant or a primary caretaker parent to participate in a residential substance abuse treatment program, even if the individual failed to disclose a substance abuse problem.