Living Shorelines Act of 2019 This bill directs the National Oceanic and Atmospheric Administration (NOAA) to award grants to state or local governments, Indian tribes, or nonprofit organizations to (1) implement climate-resilient living shoreline projects; and (2) encourage innovation in the use of natural materials to protect coastal communities, habitats, and natural system functions. In awarding grants, NOAA must prioritize projects in areas (1) where a federal disaster has been declared in the past 10 years, or (2) that have a history of coastal erosion or frequent coastal inundation in the past 10 years.