Afghan Allies Protection Act of 2019 This bill provides for 4,000 additional special immigrant visas to qualified nationals of Afghanistan who were employed by or on behalf of the United States since October 7, 2001. The visa allotment, in addition to any unused allocations of such special immigrant visas from FY2015 through FY2017, shall be available beginning FY2019, and unused visas shall carry over to subsequent fiscal years until exhausted. The Department of State Inspector General shall report to Congress on obstacles to protecting Afghan and Iraqi allies through special immigrant visa programs and recommendations for improving future programs.