I would try the following:
iOS: idevicesyslog http://stackoverflow.com/questions/7277804/ios-iphone-ipad-ipodtouch-view-real-time-console-log-terminal148

Android: adb logcat -v time

With these being both command line programs, you can Grep out the time stamp and format how you wish.

Hope this helps

We could add this data somewhere if you like. You could make a feature request in a github issue on the main appium project.

If you want to work on a pull request for this, we can work with you

Is this feature implemented in Appium?

Hi try these, it works for me

iOS: idevicedate
Android : adb shell date