Kindle Fire loads Facebook then shuts down running older windows 8 perhaps?
So the thing is that you can't install Facebook app on your Kindle?
Then try to use web version as it seems to work well.
Why use Kindle for Facebook?
This is not convenient.
PC or phone is great.
First, Kindle is OLD by now, originating first released in November 2011
for description and
In a 2012 review published by Project Gutenberg, the Kindle Fire was called a "huge step back in freedom from the Kindle 3"; the reviewer noted that Amazon introduced a "deliberate limitation" into the Fire that didn't exist in the previous version: it is no longer possible to download free e-books from websites such as Project Gutenberg, Internet Archive and Google Books and have them stored permanently in the same places where books from Amazon are kept.
IMO, it's a reader, not an internet device.