How to Find Time Constant of a BLDC Motor?
The motor will have either three or four leads. If there are four, the winding configuration is almost surely a "Y" or "wye" configuration and one of the leads is the center-point.



If you have the four-lead variety, identify the center-point by measuring the resistance between the leads. The center-point will have half the resistance to each of the other leads. Once you have identified the center-point, make note of which it is, then ignore it.

Having possibly ignored the center-point, pick any two leads. It doesn't matter which two. You can then measure the inductance and resistance between those.

For a more empirical approach to determining a suitable PWM frequency, pick one arbitrarily. Construct some means to measure the current flowing through the motor's windings. Measuring the voltage drop over a MOSFET in the drive circuitry is a reasonable approximation given \$R_{ds\_on}\$ from the datasheet. If you see the current changing significantly in a single switching period, then your PWM frequency is too low.