Does the MCUXpresso Integrated Development Environment (IDE) support the build of the TWR-KV10Z32 board demos? Or do I need the IAR tool?
The easiest way to find out if a board is going to be supported is to go to the MCUXpresso build and request a build of that board. If it's list, and the TWR-KV10Z32 is listed then you are good to go.
The TWRKV10Z is not supported by KMS though. I say this because you are in the Kinetis Motor Suite Community post area.