Flexible resistive random access memory (RRAM) devices with biomaterial gelatin and ultrathin HfOx hybrid bilayer dielectric exhibiting excellent resistive switching (RS) behavior are demonstrated. The fabricated devices show a very high memory window of greater than $10^{{5}}$ and data retention of $10^{{4}}$ s without any degradation in a pristine state. Moreover, to investigate the mechanical stability of the hybrid bilayer film and variation in switching performance upon bending was studied by bending the devices at a 12-mm radius followed by 7 mm. Even after this extreme bending, the device maintained the memory window of $10^{{5}}$ without any degradation in data retention, indicating excellent electromechanical stability of the device. Furthermore, a simple mathematical model of the RRAM device was used to simulate these devices with the help of our experimental data and the ${I}$ – ${V}$ equations. The developed model shows excellent accuracy with a relative root mean square (RMS) error of less than 5%, which can prove to be an excellent tool for the simulation of circuits and systems based on these RRAMs.