The SMC drivers allow Kinetis SDK projects to go into low power modes, take a look at the SMC_SetPowerMode<mode> API, there are Selectable wakeup sources.
See the power mode examples in your KSDK tree for details:
−\boards\<board_name>\demo_apps\power_manager
−\boards\<board_name>\demo_apps\power_mode_switch
Using another type of MCU I have developed several low power devices running on 1/2 AA batteries , however not on Kinetis (yet).
I would approach it based on similar principles where the software regularly switches between the Low Power modes when interrupted by a timer or other interrupt source. Implementing software this way requires some forethought on design.