This help page at amazon.com has instructions for sideloading content onto a Fire tablet. Different media goes to different directories:
Quote:
(Abridged)
1. From your computer, locate the content you want to transfer from your computer to your Fire Tablet.
2. Connect your device to your computer with the micro-USB cable that came with your device. If you've set a lock screen password on your device, you may need to unlock your device before it can be opened on your computer.
3. Open the device folder (titled Fire) on your computer, and then open the Internal storage folder.
4. Locate the downloaded file on your computer, and then drag and drop the compatible file you want to transfer into the applicable folder:
Audiobooks: AA, AAX
Books: AZW (.azw3), MOBI (non-DRM), KF8
Documents: TXT, PDF, PRC, DOC, DOCX, HTML5, CSS3
Music: MP3, non-DRM AAC (.m4a), MIDI, PCM/WAVE, OGG, WAV, AC-3, E-AC-3, AMR-NB, AMR-WB
Pictures: JPEG, GIF, PNG, BMP
Movies: MP4, 3GP, VP8 (.webm), M4V, MKV
5. Disconnect your device from your computer.
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ETA: Fire tablet owners can use the Manage Your Content and Devices page at Amazon to download books directly to their PC and then sideload them. (The usefulness of this is limited, but it does provide a way to load your books into calibre.)