This article is concerned with the influences of the pressure work and Hall currents on the motion of a non-Newtonian nanofluid with heat and mass transfer inside a vertical symmetric channel. The fluid conforms to the Bingham–Papanastasiou model. The walls of the channel are assumed to be flexible, movable and sinusoidal. Thermal radiation, heat generation/absorption and chemical reaction are thus considered. Concerning the assumptions of the long wavelength and low Reynolds number, the resulting equations are solved by utilising the homotopy perturbation method (HPM). The succeeding complex computations are clarified for the stream flow, temperature and concentration distributions. A set of graphs is plotted to illustrate the effects of various physical parameters of the problem at hand. It is found that as the Bingham factor is increased, both axial velocity and temperature are also increased. Additionally, it is observed that the stress growth exponent has a dual influence on the axial velocity as well as the size of the trapped bolus. The behaviour of the left wall of the channel is different from that of the right wall. When the pressure work and Hall current coefficients increase, both temperature and pressure gradient decrease. The Brownian motion and thermophoresis parameters have different influence on the nanoparticle concentration distribution. Furthermore, it is shown that the heat transfer coefficient is a decreasing function in both Hall and thermal radiation parameters.