Novel flavanones that incorporate chromene motifs are synthesized via a one-step multicomponent reaction. The structures of the new chromenes are elucidated by using IR, 1H-NMR, 13C-NMR, 1H-1H COSY, HSQC, HMBC, and elemental analysis. The new compounds are screened for their in vitro antimicrobial and cytotoxic activities. The antimicrobial properties are investigated and established against seven human pathogens, employing the agar well diffusion method and the minimum inhibitory concentrations. A majority of the assessed derivatives are found to exhibit significant antimicrobial activities against most bacterial strains, in comparison to standard reference drugs. Moreover, their cytotoxicity is appraised against four different human carcinoma cell lines: human colon carcinoma (HCT-116), human hepatocellular carcinoma (HepG-2), human breast adenocarcinoma (MCF-7), and adenocarcinoma human alveolar basal epithelial cell (A-549). All the desired compounds are subjected to in-silico studies, forecasting their drug likeness, bioactivity, and the absorption, distribution, metabolism, and excretion (ADME) properties prior to their synthetic assembly. The in-silico molecular docking evaluation of all the targeted derivatives is undertaken on gyrase B and the cyclin-dependent kinase. The in-silico predicted outcomes were endorsed by the in vitro studies.