We perform nonequilibrium molecular dynamics simulations to examine the change in orientational order of a ferroelectric nematic liquid crystal under shear flow, specifically planar Couette flow. The orientational order is found to decrease with increasing shear rate. This drop in orientational order is not due to structural changes but is rather a result of the director dynamics being flow unstable. Employing both nonequilibrium and equilibrium molecular dynamics with the director orientation fixed, we determine the shear and twist viscosities which relate the pressure tensor to the shear or strain rate tensor in a nematic liquid crystal under flow. The Miesowicz viscosities are then obtained from linear combinations of the shear and twist viscosities. The short-range spatial structure of the ferroelectric nematic liquid crystal is similar to that of a ferroelectric tetragonal I lattice. The relative magnitudes of the Miesowicz viscosities can be understood by examining the shear stress response of this lattice to a shear deformation.