Law Enforcement Trust and Integrity Act of 2019 This bill requires the Department of Justice (DOJ) to take specified steps to address accreditation standards, management operations, and misconduct of law enforcement. Specifically, it requires DOJ to develop uniform accreditation standards for law enforcement agencies and adopt policies and procedures to encourage law enforcement agencies to pursue accreditation. It authorizes DOJ to make grants to law enforcement agencies to obtain accreditation from certified organizations. The bill authorizes DOJ to make grants for studying law enforcement agency management and operations standards and developing pilot programs to address law enforcement misconduct. DOJ must study the prevalence and effect of any law, rule, or procedure that allows a law enforcement officer to delay the investigation and prosecution of complaints of law enforcement misconduct. The bill also establishes the Task Force on Law Enforcement Oversight to coordinate the detection and referral of complaints of alleged law enforcement misconduct. Law enforcement agencies must report data regarding practices on traffic violation stops, pedestrian stops, frisk and body searches, and use of deadly force. Finally, DOJ must create a medallion for survivors of each law enforcement officer killed in the line of duty and memorialized on the wall of the National Law Enforcement Officers Memorial.