In this work, the temperature dependence of the viscosity and thermal conductivity of molten systems FLiNaK and FLiNaK-MeF3 (Me = La, Nd) was studied using the molecular dynamics method with Born-Mayer-Huggins potential. The dependencies were obtained in the temperature range of 800 < T < 1020 K, as well as for the concentration of lanthanide fluoride additives up to 15 mol.%. The temperature behavior of these kinetic properties is explained based on an MD model of dynamic ionic connectivity. The main contribution to the connectivity of pure FLiNaK ions is made by Li-F ion pairs, and in the presence of LaF3 and NdF3 dissolved in the salt mixture, the connectivity in the system is supplemented by ion pairs formed by lanthanides with fluorine. Both viscosity and thermal conductivity decrease with increasing temperature and rise when lanthanide trifluorides are added to the molten salt.