Tribal HUD-VASH Act of 2019 This bill provides statutory authority for the Tribal HUD-VASH program, which provides rental assistance and supportive services to Native American veterans who are homeless or at risk of homelessness and living in or near an area where a tribe or tribally designated housing entity provides assistance for affordable housing. The Department of Housing and Urban Development (HUD) is directed to use at least 5% of rental assistance amounts under the HUD-VASH program, which provides housing assistance to homeless veterans, for the Tribal HUD-VASH program. The Tribal HUD-VASH program shall be carried out in conjunction with the Department of Veterans Affairs (VA). HUD and the VA shall consult with tribal organizations regarding the program's design and may make program modifications after consulting with tribal organizations. Program grants shall be made to entities eligible for Native American housing assistance block grants. HUD may make renewal grants to entities that have received prior program grants.