I moved your post to a new thread, since it seems to be about a new topic.
I am not very familiar with the ARM mbed FRDM-KL25Z board, but according to its product page on the ARMmbed website, the board has many interfaces (e.g. UART) that you could use to communicate with the Arduino Uno, so yes, it is possible. Choosing an appropriate communication protocol will depend on your application. You might consider posting your question on mbed's forum, as it has a much larger community and focus specifically on mbed boards.