For the first time, kinetic thermomagnetic extraction is a novel approach presented in this work. It required the application of four distinct variables: rotation speed (50, 75, and 100 rpm), magnetic field (0.8, 1.2, and 1.6 T), time interval (30, 60, and 90 min), and temperature (45, 55, and 65°C). Numerous phytochemical categories were detected in the 81 crude chloroform extracts of green sweet bell pepper seeds that were collected, according to phytochemical analysis. Nine extracts were discovered to be linked to the coumarin chemical class and to have the same two extraction parameters: a 90‐minute extraction duration and a 55°C extraction temperature. To enable their coumarin contents to be chemically separated and chromatographically purified, two of these extracts containing coumarin were chosen. Four new phytocoumarins have been identified and their molecular structures distinguished using FTIR spectra, 1H‐NMR, 13C‐NMR, and mass analysis. The results demonstrated that the extracted phytocoumarins have exceptional oxidative stress‐mitigating characteristics, ranging from 71.51 to 81.48%, when compared to a positive control. Furthermore, they showed excellent cytotoxicity against the test malignant populations (IC50 values of 46.76–81.45 μg/ml). The isolates need to be taken into account as dual COX‐2/5‐LOX antagonists because they also showed a selective anti‐inflammatory effect