As a novel low GWP working fluid 1,1,3,3,3-hexafluoro-2-methoxypropane (HFE-356mmz) is regarded as a promising candidate for high-temperature heat pumps and organic Rankine cycle. Recently, the experimental kinematic viscosity and thermal conductivity data of HFE-356mmz were published in the literature. However, at the time of that publication it was not possible to develop any mathematical model of the transport properties due to unavailability of an equation of state. In this work, we report dynamic viscosity data of HFE-356mmz together with mathematical models for dynamic viscosity and thermal conductivity using the extended corresponding states (ECS) and the residual entropy scaling (RES) technique. With R134a used as the reference fluid for ECS method, the transport shape factors and the other adjustable parameters were calculated by utilizing latest multi-parameter Helmholtz-energy-explicit-type equations of state for HFE-356mmz. Furthermore, slight modification of the original RES method has been adopted that removes the implicit dependency on the tuned ECS method. By using the adjustable parameters, the tuned ECS and RES transport equations can represent the experimental data within reported uncertainties. The average absolute deviations (AAD) for viscosity and thermal conductivity were found to be 0.85% and 0.76% using the tuned ECS and 0.83% and 0.44% using the modified RES method respectively.