Rapidly spreading viral pandemics, such as those caused by influenza and SAR-CoV-2 (COVID19), require rapid action and the fastest way to combat this challenge is by repurposing existing drugs as anti-viral therapeutics. Here we first show that human organ-on-a-chip (Organ Chip) microfluidic culture devices lined by a highly differentiated, primary, human lung airway epithelium cultured under an air-liquid interface and fed by continuous medium flow can be used to model virus entry, replication, strain-dependent virulence, host cytokine production, and recruitment of circulating immune cells in response to infection by influenza, as well as effects of existing and novel therapeutics. These Airway Chips, which contain human lung epithelial cells that express high levels of ACE2 and TMPRSS2, were then used to assess the inhibitory activities of 7 clinically approved drugs (chloroquine, arbidol, toremifene, clomiphene, amodiaquine, verapamil, and amiodarone) that we found inhibit infection by viral pseudoparticles expressing SARS-CoV-2 spike protein in human Huh-7 cells, and others recently showed suppress infection by native SARS-CoV-2 in Vero cells. However, when these drugs were administered under flow at the maximal concentration in blood reported in clinical studies in human Airway Chips, only two of these drugs - amodiaquine and toremifene - significantly inhibited entry of the pseudotyped SARS-CoV-2 virus. This work suggests that human Organ Chip technology may be used in conjunction with existing rapid cell-based screening assays to study human disease pathogenesis and expedite drug repurposing in biothreat crises caused by pandemic viruses.