In this article, diffusion-thermo, thermal radiation, and first-order chemical reaction effects are studied analytically when the aligned magnetic field set to the fluid/ the plate on the unsteady, free convective fluid passing through an inclined vertical plate by flexible surface conditions, concentration diffusion under the action of a coaxial magnetic field. The governing PDE's are derived from the physical model and transformed into dimensionless form. Then a closed-form solution is obtained using the Laplace transform method. The effects of controlling parametric quantities like M, R, Sc, Pr, Du, Gr, Gm are analyzed through graphs for fluid properties. A comparative study has been made with published results in the absence of some non-dimensional parameters for a particular case (aligned magnetic field set to the fluid) found in good agreement.