Power consumption of devices and implications around designing on embedded systems is a common topic nowadays. Kinetis MCUs offer different power modes to fit user's needs. Among these low power modes, we can find the lowest consumption modes: Low-Leakage Stop (LLS) and Very Low-Leakage Stop modes (VLLS).
Attached document provides a brief introduction/explanation on these modes and lists the steps needed to configure MCU to operate in any of these modes. It is a bare-board project for FRDM-KL26Z but same principle applies to other Kinetis families. Also, two projects for KDS v3.2 are attached for reference.
I hope you can find them useful!