There is no flight mode option on the Liberty watch phone.  You can simply power off the watch when going on a flight by gently pressing a pin into the reset pinhole – see number 5 in the image below.

When you reach your destination you can power back on the watch and wait a couple of minutes to allow the watch to adjust to a new time zone, if applicable.  If you do not turn off the watch and change time zones, you may need to reset the watch by powering it off, to set the time correctly.