FET Switching Loss in BLDC Inverter
Even with high switching current, the average gate current will be quite low, essentially zero except during each instance of switching.  Calculating switching time is always tricky, because of the way parts are specified.  The driver max current values for this part are measured at 2V (source) and 8V (sink), and the minimum gate drive voltage is not specified at this current but at a lower current. TI does not give any curves for this part, only a few discrete points.  The FET looks reasonable with its input and reverse transfer capacitance values.  So, an accurate calculation of switching time is not really feasible.

Having sais this, you should expect switching times in the hundreds of nanoseconds rather than the 19 uS you have estimated.  You can adjust the switching time with a series resistor on the gate drive, although this may not be needed since the part has built-in dead time.  Make the FET traces wide and short, including the gate, to avoid inductance.