Military Special Victims Protection Act of 2019 This bill modifies and establishes requirements relating to the prosecution of sexual misconduct and domestic violence in the Armed Forces, including by restricting initial case determinations to officers of at least a certain grade with special authority and by requiring additional review of certain decisions. The bill also expands legal services and options for victims, including by allowing certain victims who were discharged from service to correct their military records with respect to specified mental health diagnoses.