If you have a pdf file that isn't larger than your email provider will allow, you can attach it and email it to yourself. Pick up the email on your Kindle Fire and "open" the attachment. You don't even need to send it to your special Kindle email address… Send it to yourself to your normal email address, then open your Kindle and do a quick email run (if you have gmail, you can go to gmail.com with the browser and check).
You're going to love this next part….
Once you have the email displayed on your Kindle Fire, touch the Open button to the right of the attachment and let your Kindle Fire download it. If you choose Save, your file will be sent to a download folder. You can find it any time with other software there.
The next little dialog you will see will offer you choices (some may see more than others) of apps you can open the file with. Choose Kindle. Your Kindle reading app will open and you can peruse that pdf at your leisure.
Oh... I did notice using these choices, your pdf file will NOT be saved in your Kindle docs. When you leave your Kindle app, then return to it later, you will need to re download the file and open it in your Kindle app. The only way I could see to "store" it there was to physically transfer the pdf file via usb to the documents folder. Another way would be to email it to your special Kindle email address.