I would think any WiFi and/or 3G/4G capability can be switched off. Do that and you are in Flight Safe Mode, although it is not labelled as such a state, if I am not mistaken.
Sorry, I assume you meant to say "How do I switch aeroplane mode on....", but if you actually have one that has a flight mode labelled as such then I am stumped because I don't know about this - maybe select flight mode and click on it again ??
Sorry for the late reply. it's an old kindle. AEROPLANE MODE turn on aeroplane mode to disable wireless connectivity. Turn on. When selected turn off is displayed it will return to turn on.Back to square one. I hope that is clear? It's obviously comming from someone who has no idea what he is talking about. Please bear with me.
Go into settings via the second button from right. Select Aeroplane Mode. It can be switched between "turn on" and "turn off" by pressing the middle button.