Fair Day in Court for Kids Act of 2019 This bill authorizes the Department of Justice (DOJ) to appoint or provide counsel, at the government's expense, to aliens in removal proceedings and related appeals. An unaccompanied alien child shall be represented by counsel paid for and appointed by the government at every stage of such proceedings. The Department of Homeland Security (DHS) shall provide a complete copy of an alien's immigration file to the alien (or the alien's counsel) within seven days of a notice to appear for an immigration proceeding, and failure to provide the file shall result in a delay in the proceeding. DHS shall provide access to counsel for all detained aliens. The bill authorizes the DOJ to enter into contacts or award grants for providing immigration-related legal services to children. The Executive Office for Immigration Review shall develop model guidelines for representing alien children in immigration proceedings.