I have been experimenting with the RTC in the KL parts; for example, on a KL46 board - but the behaviour seems the same on all KLs.
I also checked out this tutorial:Using RTC module on FRDM-KL25Z
There are two of things that are weird:
1. According to the KL46 user's manual the 32kHz crystal oscillator can be enabled by SW - OSCE in RCT_CR, however if this is tried the device fails and can't select the normal crystal clock input to start until a power cycle occurs. Presumably this is an error in the user's manual since the devices don't support a 32kHz crystal oscillator (?)
2. According to the user's manual the default clock is OSC32KCLK however the RTC only counts when the LPO 1kHz input is selected or a clock is applied to RTC_CLKIN and this is selected as input (OSC32KSEL in SIM_SOPT1). It is as if there is either no OSC32KCLK available or it can't be enabled?). This seems to be backed up to some degree by the turorial linked above since it generates a 32KHz clock on RTC_OUT and physically wires it back to RTC_CLKIN, which seems a lot of effort to go to if the RTC has a default 32kHz clock from the OSC as the user's manual suggests.
Is the OSC32KCLK available??