<p>Hybrid nanofluid has gained a lot of attention from researchers in the current generation of fluid technology because of its potential and thermal characteristics, which improve the rate of heat transfer more effectively than nanofluid. Applications for hybrid nanofluids in engineering, industrial, and medical research include biological disciplines, drug, and cooling operations. Therefore, the current study examines the mass and heat transfer in Boger hybrid nanofluid circulation across a moving flat plate while accounting for linear thermal radiation and nonlinear thermal radiation with the Blasius and Sakiadis flows. The magnetic field and chemical reaction impacts are also considered. By utilizing an appropriate similarity transformation, the collection of PDEs (partial differential equations) are modified into ODEs (ordinary differential equations). The Runge–Kutta-Fehlberg-45 (RKF-45) order approach and shooting technique are employed to solve the resulting ODEs. Also examined the significant engineering quantities. The important results of this work illustrate that the velocity profile will improve by elevating the values of the solvent fraction constraint in the case of Sakiadis flow, and the opposite action in the Blasius flow. In the case of Sakiadis and Blasius flows, the temperature profile elevates as the radiation constraint value increases for both linear and non-linear thermal radiation. For both cases (Blasius and Sakiadis flows), the Nusselt number will rise as the radiation constraint and magnetic constraint values increase.</p>