American Dream and Promise Act of 2019 This bill cancels and prohibits removal proceedings against certain aliens and provides such aliens with a path toward permanent resident status. The Department of Homeland Security (DHS) or the Department of Justice (DOJ) shall cancel removal proceedings against certain aliens who entered the United States as minors and grant such aliens conditional permanent residence status for 10 years. The bill imposes various qualification requirements, such as the alien being continuously physically present in the United States and being enrolled in or having completed certain educational programs. DHS shall establish streamlined procedures to apply for conditional permanent residence for aliens who received Deferred Action for Childhood Arrivals (DACA) status and were not disqualified for renewal. DHS shall remove the conditional permanent resident status granted to such aliens, if the alien applies and meets certain requirements, such as completing certain programs at an educational institution or serving at least two years in the Uniformed Services and being discharged honorably. DHS or DOJ shall cancel removal proceedings against certain aliens who qualified for temporary protected status or deferred enforced departure status on certain past dates (both statuses temporarily protect covered aliens from removal). For such aliens who apply and pass the required background checks, DHS shall grant permanent residence status. DHS may not use information from applications to adjust status under this bill for immigration enforcement purposes. DHS shall establish a grant program for nonprofit organizations that assist individuals with certain immigration-related issues.