In this study we use the spectral relaxation method (SRM) for the solution of the steady von Kármán flow of a Reiner-Rivlin fluid with Joule heating and viscous dissipation. The spectral relaxation method is a new Chebyshev spectral collocation based iteration method that is developed from the Gauss-Seidel idea of decoupling systems of equations. In this work, we investigate the applicability of the method in solving strongly nonlinear boundary value problems of von Kármán flow type. The SRM results are validated against previous results present in the literature and with those obtained using the bvp4c, a MATLAB inbuilt routine for solving boundary value problems. The study highlights the accuracy and efficiency of the proposed SRM method in solving highly nonlinear boundary layer type equations.