Equilibrium molecular dynamics (EMD) Green-Kubo simulations of the shear viscosity coefficient of molten sodium chloride and potassium chloride are reported in the microcanonical ensemble (N,V,E). The potential model used is the Born-Mayer-Huggins-Tosi-Fumi interionic potential, and several state points have been investigated. The form of the stress tensor elements for ionic fluids whose electrostatic interactions are calculated through the Ewald method is discussed in detail. The results show that the agreement between the simulation and the available experimental data is satisfactory, and the viscosity is overpredicted (generally to within 10%-15%).