Don't know what "sinking current into" means. I guess you want to estimate the additional gate driver load caused by a TVS diode. For an exact calculation, you need to know the diode C/V characteristic. For a first estimation, you can calculate with the diode capacitance at actual gate voltage, slightly higher than C(VR).
If TVS diodes actually provide any protection for your MOSFET and IGBT is a different question.