Understanding dynamic human mobility changes and spatial interaction patterns at different geographic scales is crucial for assessing the impacts of non-pharmaceutical interventions (such as stay-at-home orders) during the COVID-19 pandemic. In this data descriptor, we introduce a regularly-updated multiscale dynamic human mobility flow dataset across the United States, with data starting from March 1st, 2020. By analysing millions of anonymous mobile phone users' visits to various places provided by SafeGraph, the daily and weekly dynamic origin-to-destination (O-D) population flows are computed, aggregated, and inferred at three geographic scales: census tract, county, and state. There is high correlation between our mobility flow dataset and openly available data sources, which shows the reliability of the produced data. Such a high spatiotemporal resolution human mobility flow dataset at different geographic scales over time may help monitor epidemic spreading dynamics, inform public health policy, and deepen our understanding of human behaviour changes under the unprecedented public health crisis. This up-to-date O-D flow open data can support many other social sensing and transportation applications.