You can easily measure Cp by a standard DSC method (cooling down, equilibrating and scanning with heating rate 10 C/min). At the same time, the device should be calibrated for Cp before you will start the experiments. Also, keep in mind that the thermal history of the sample may influence a lot on the Cp value. I would recommend you to check the manual for your device, it is always written some important information there concerning accuracy and required measures. In the case of thermal conductivity it is a bit technically difficult and not all the models of DSCs can measure it.
This is discussed here very often. To my experience, you cannot get better uncertainty than some 30% for Cp measurements with DSC. If you had a power-compensated DSC or PPMS system, the uncertainty could lower to some 5%. Uncertainty about 1% can be reached using a Tina-Calvet DSC calorimeter. Even lower, you need an Adiabatic one.