Joint Long-Term Storage Act of 2019 This bill requires the Advanced Research Projects Agency-Energy (ARPA-E) in the Department of Energy to establish a demonstration initiative composed of demonstration projects focused on the development of long-duration energy storage technologies. The goals of the initiative include demonstrating the potential benefits of long-duration energy storage to efficient use of the electricity grid and increasing the commercial viability of long-duration energy storage technologies. As part of the initiative, ARPA-E must establish a joint program with the Department of Defense's Environmental Security Technology Certification Program office to (1) demonstrate promising long-duration energy storage technologies at different scales; and (2) help new, innovative long-duration energy storage technologies become commercially viable. The bill authorizes through FY2024 the Duration Addition to electricitY Storage program to develop energy storage systems that provide power to the electric grid for durations of 10 to approximately 100 hours.