Gun Safety Board and Research Act This bill establishes a gun safety board in the Department of Health and Human Services. The board must (1) conduct original research about firearm violence reduction; (2) publish policy recommendations for and findings about the efficacy of federal, state, and local actions to reduce firearm violence; and (3) establish a grant program to support original research on firearm violence reduction and education for the public about the effects of and ways to mitigate firearm violence.