Flaviviruses are among the most critical pathogens in tropical regions; they cause various severe diseases in developing countries but are not restricted to these countries. The development of antiviral therapeutics is crucial for managing flavivirus outbreaks. Ten proteins are encoded in the flavivirus RNA. The N2B–NS3pro protein complex plays a fundamental role in flavivirus replication and is a promising drug target; however, no flavivirus protease inhibitors have progressed to the preclinical stage. This study analyzed the structural models and plasticity of the NS2B–NS3pro protein complex of five medically important non-dengue flaviviruses (West Nile, Rocio, Ilhéus, yellow fever, and Saint Louis encephalitis). The flavonoids amentoflavone, tetrahydrorobustaflavone, and quercetin were selected for their exceptional binding energies as potential inhibitors of the NS2B–NS3pro protein complex. AutoDock Vina results ranged from −7.0 kcal/mol to −11.5 kcal/mol and the compounds preferentially acted non-competitively. Additionally, the first structural model for the NS2B–NS3pro protein complex was proposed for Ilhéus and Rocio viruses. The NS2B–NS3pro protease is an attractive molecular target for drug development. The three identified natural flavonoids showed great inhibitory potential against the viral species. Nevertheless, further in silico and in vitro studies are required to obtain more information regarding NS2B–NS3pro inhibition by these flavonoids and their therapeutic potential.