Synthetic drugs such as allopurinol and benzbromarone are commonly used to treat the complex pathogenesis of gout, a metabolic disease that results from an inflammation of the joints caused by precipitation of uric acid. We seek to discover novel phytochemicals that could treat gout, by targeting the xanthine oxidase and cyclooxygenase-2 enzymes. In this study, we report the screening of nine compounds of flavonoids from the ZINC and PubChem databases (containing 2092 flavonoids) using the igemdock software tool against the xanthine oxidase and cyclooxygenase-2 3D protein structures. Each compound was also evaluated by an in vitro bioassay testing the inhibition of xanthine oxidase and cyclooxygenase-2. Myricetin and luteolin were found to be the potential dual inhibitors of xanthine oxidase and cyclooxygenase-2 as demonstrated by IC50: 62.7 and 3.29 μg/mL (xanthine oxidase)/70.8 and 16.38 μg/mL (cyclooxygenase-2), respectively. In addition, structure–activity relationships and other important factors of the flavonoids binding to the active site of xanthine oxidase and cyclooxygenase-2 were discussed, which is expected for further rational drug design.