Hi Ivan Rusnacko,
Sorry for our late reply!
According to the datasheet of KL05,48MHz core/24MHz bus and flash, in run mode,

the 6.3mA consumption is normal,and when test, the condition should be take care, like the following picture:

I think if you want to test the consumption of KL05, you can test the demo code "low_power_demo" , after my test FRDM-KL05, the consumption is consist with the datasheet.
You can download the demo code from this link:
http://www.freescale.com/webapp/sps/download/license.jsp?colCode=KL05-SC&location=null&fpsp=1&WT_TYP... and Test Software&WT_VENDOR=FREESCALE&WT_FILE_FORMAT=zip&WT_ASSET=Downloads&sr=8&Parent_nodeId=1359130311707695721244&Parent_pageType=product
BTW, I didn't find the consumption of 16Mhz core frequence in run mode from the datasheet, so maybe your test should switch to 48MHz, and the compare the result with table 5 in the datasheet.
I wish it helps you!
Best regards!
Jingjing