Vaccine Fairness Act of 2020 This bill requires the Department of Health and Human Services (HHS) to provide weekly reports to Congress concerning the distribution of COVID-19 (i.e., coronavirus disease 2019) vaccines to the public. Specifically, HHS must submit the first report within seven days of the date on which the federal government begins distributing COVID-19 vaccines. Additionally, the Secretary of HHS must be available to brief Congress on the date on which each report is submitted.