They've got some information about the storage on the Fire SD card
here.
You can install apps and games, download music, videos, and audiobooks, and store photos and personal videos on an external MicroSD Card. Books, Silk browser downloads, and email can only be downloaded to and stored on the internal storage of your Fire tablet.
When they say "books" I think they mean books downloaded from Amazon. I have my whole library on the SD card, in epub format, on the SD card and they open in EZ and Aldiko.
I also think that for the things you can 'download' they mean that you can point apps to download those items to that space. (I think it's in the settings somewhere that you can point apps to us that space instead of internal storage.) But app access doesn't mean you can 'sideload' that media yourself. It's just for app use.
I'd point the video apps to that space, download something, then see if it's visible on the SD card. If it is, then maybe you can sneak other files there, but the app may never see them since they're not listed in their inventory.
But you might find it works if you pay with it that way.