In this paper, we have discussed the MHD peristaltic flow of Al2O3 − Cu/H2O hybrid nanomaterial in a channel whose walls are taken to be compliant in nature. We also examined the effects of joule heating, thermal slip boundary conditions, thermal radiation, hall current, porous medium, heat source/sink, and viscous dissipation. The flow rotates at a constant angular velocity. The main aim of this work is to study the effects of various physical parameters on the peristaltic flow of a hybrid nanofluid in a rotating channel with complaint walls and heat transfer. The model is presented by using the conservation laws of mass, momentum, and energy along with boundary conditions. Selected variables have been used to simplify the nonlinear equation and the hypotheses of large wavelengths and small Reynolds numbers. The simplified form of the system of equations is solved using Adam’s Bashforth method, which is a multistep predictor–corrector method. To explore the potential applications of hybrid nanofluids in biomedical engineering, nanotechnology, and industrial processes, the effects of emerging parameters on both axial and secondary velocities and the temperature profile are analyzed with the help of graphs. The flow and temperature profiles are influenced by the hall effect, magnetic field, thermal slip, thermal radiation, viscous dissipation, porous medium, and heat source/sink parameters. We find that both velocities increase with hall effect and first-order slippage but decrease with magnetic field parameter. The temperature of the nanoparticles increases with dissipation effects but decreases with thermal radiation.