Typically Airplane Mode will turn off all built in radios within the device such as WiFi, Bluetooth, and Cellular. The Kindle Fire HD 7" doesn't have a cellular radio but Airplane Mode should turn off both WiFi and Bluetooth.

When the airplane icon appears on the menu bar, you can easily show that to a flight attendant on an airplane if s/he asks you to verify your Kindle is in Airplane Mode.

OFF TOPIC: The FCC is now saying that they find no reason to prohibit cellular phones from being used on airplanes. After all the electronics on airplanes are extremely well insulated from interference. So perhaps before too many more years the FAA and airlines will lift the restrictions making Airplane Mode a thing of the past.