How to put the Kindle Fire in airplane mode?
On the original Kindle Fire Airplane mode does not seem to exist, but you can turn off wireless using these directions:


Tap the Quick Settings (the Gear) icon in the top right hand corner of the Home screen.
Tap Wi-Fi.
Ensure Wireless Networking switch is in the off position.


On the new Kindle Fire you can enable airplane mode by doing the following:


Swipe down from the top of the screen and tap Wireless.
Tap On next to Airplane Mode