Hello Kasra Haghighi:
I am sorry for the long time with your unanswered question.
About MBED, yes, the libraries should be compatible within devices of the same family, and MBED for Kinetis is actually based on KSDK.
PS. While this community is a good place to discuss about Kinetis enablement, you may also want to participate in the MBED dedicated community:
MBED_Forum
Regards!
Jorge Gonzalez