Protecting Americans from Seasonal Influenza Act of 2020 This bill requires the Centers for Disease Control and Prevention to award grants to increase seasonable influenza vaccination rates in states that have sustained influenza vaccination rates below recommended levels. State health agencies receiving such grants must include at least one of the elements set out in the bill in their programs. Among others, these include (1) increasing outreach to vulnerable populations, (2) encouraging employer-based vaccination programs, and (3) coordinating between health care providers and insurers to reduce out-of-pocket costs of vaccinations.