Under the "docs" on the Kindle fire, there is a Fire Users Guide...
On the very first few pages is a section called "Kindle Fire hardware"
In that section it tells the 3 ways to turn off the Fire.
1) press and release. for "sleep mode"
2) Press hold till you get the message to shut down. to "turn off"
3) Press and hold for 20 seconds... release after it shuts down...
then press to turn on again. This is recommended for when/if
the device becomes unresponsive.
I also use this when I install a new app that does not appear to be behaving properly.