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The recent hypothetical analysis is to explore the effect of hall current and ion's slip for a peristaltic mechanism of non-Newtonian Rabinowitsch fluid model (lubricant blended with the viscosity index reformer) with the dynamic damping and stiffness features. The mathematical model is examined by considering the assumptions of low Reynold's number and long wavelength, the governing system of non-linear differential equations are solved with the help of the perturbation technique. The impact of numerous parameters associated with a fluid flow such as viscous damping, stiffness, rigidity, Hall parameter and Brickman number are intrigued for velocity profile, temperature distribution, and concentration profile. Results are strategized and deliberated for shear thickening, shear-thinning, and a viscous fluid model. It is observed that the momentum distribution is enhanced for larger values of stiffness, rigidity and viscous damping force parameters, but quite reverse nature is depicted for thermal distribution. The variations of streamline are presented graphically for the Hartman number and elastic parameters. Brinkman number is related to the viscous dissipation effects, so it contributes to enhancing the thermal distribution of fluid for all cases.