Glad to meet you Luciano,
The KV series of MCUs including the three you mentioned, the KV1x, the KV3x, and the KV4x MCUs call all drive a BLDC or PMSM motor. The BLDC motor, as Adam mentioned can be driven with a standard 6-step commutation algorythm or a sensorless (back EMF) method or with sensorless FOC. There are two basic motor control options from NXP, 1) the Kinetis Motor Suite - which uses a sensorless FOC algorythm or 2) a Kinetis Motor control reference design. For people without a lot of motor control expertise the KMS offers a tuning ability to get the motor running.
The KV3x MCU family includes four devices ranging in size and speed from a 512K flash 120Mhz part down to a 64K flash 100 MHz part. Any of them can be used with KMS. The MKV31F512xxx12 is what is used on the MCU evaluation boards as a superset part of the MCU family. In you end application you can utilize any one of the four MCU parts.
The
MKV30F128VLF10P ,
MKV31F128VLH10P ,
MKV31F256VLH12P , or the
MKV31F512VLL12P
Your choice of the most expensive of these, the 512K part would only be driven if your application code, added to the motor control reference project (KMS takes approximately ~64K), takes up the rest of the flash.
If your code was very small and it and the KMS software fit into the less expensive 128K flash MCU.
There are instructions in the KMS documentation as to how to change the reference project to the other devices.
Since your application is a High voltage application, you could use the design of the HVP KV31 board for your testing. Those boards include the same KV31F512 with KMS pre-programmed on it. One of the key differences is the opto-isolation between the MCU drive and the debugger hardware on the board. You can see this HVP platform here
, The part number of the KV31 controller card is HVP-KV31F120M, it's available from nxp.com for $79.00, with a User's Guide and the design files and schematics available in the HVP download tab.

I hope this helps.
Best Regards,
Philip