I can’t play my Facebook games on my Kindle Fire, such as Candy Crush Saga or any others on Facebook.
I take it you mean that the games are not in the Amazon App store, correct? If you mean that you can download another free app store. I use 1mobile and was able to download them from there.
Flash games won't work without some effort, and there's no native version of CC for the Fire. Sorry...
If you don't want to hassle with installing Flash player try Photon Flash Player & Browser at https://play.google.com/store/apps/details?id=com.appsverse.photon
Unfortunately, Facebook games are not designed for Android or touchscreen devices in mind, at least not yet. There are some apps in the Play Store that allows for Facebook connection, such as Candy Crush Saga, Words With Friends, etc. The very basic games may be able to be played through the browser like Farmville, but if there is too much for the browser to load, then the game will either not load completely or freeze. There are more games becoming available for Android devices in the Play Store, so I would do searches to see if the game you wish to play are available.
you have to install Dolphin HD web browser and Adobe flash player to play flash games
How to Install Adobe Flash Player on the Kindle Fire HD
How to install Flash Player on Kindle Fire HD, Step-by-Step guide to play Flash videos at Youtube and to watch Network TV episodes. UPDATED