Magnetofluiddynamics (MFD) is an emerging and interesting scientific area with various industrial and medical applications such as monitoring the blood flow, power generator, wire and fiber coating, geothermal reservoirs, magnetic drug targeting and cell separation. In view of significance of the magnetic field in the industrial and medical sciences, the current study focusses the effect of magnetohydrodynamics and modified Darcy's law on the viscoelastic nanofluid flow under various effects such as electroosmosis, thermal radiation, Hall currents and slip boundary conditions. We have considered the equations governing the flow problem in Cartesian coordinate system. The governing equations for the nanofluid flow have been simplified by using appropriate assumptions and nondimensional quantities, and provided the closed form solutions for the velocity, temperature and nanoparticle volume fraction profiles. Later, the numerical simulations are presented for diverse parameters on the various flow quantities. The current results reveal that, the velocity deduces with enhancing the strength of the magnetic field and it enhances with respect to solute Grashof number, and the temperature decreases with increase of radiation effects. The current analysis is relevant to electrokinetic hemodynamics and microfluidics.