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Welcome to The forums! I am sorry you are having issues downloading your videos to your FireTablets. Let's try this!
Please make sure that you have a strong Wi-Fi connection and sufficient bandwidth.
Return to the video detail page and tap "Options." Select "Cancel download," and then tap "Download" to try again.
If the issue persists, restart your device by pressing and holding the power button for up to 40 seconds until the screen goes black.
Once your device has restarted, return to the video detail page and press "Download."
After your video has been downloaded to your device or SD card, you can find it in your video library.
For Kindle Fire 1st and 2nd Generation:
To view all videos downloaded to your Fire tablet, tap "Videos" from your home screen, tap "Library." and then open the "Device" tab
For all other Fire Tablets:
Tap "Videos" from your home screen. Swipe left to open the menu, or tap the "Menu" button, and then select "Your Downloads."
-You can also open "Your Video Library" from the menu and select the "Device" option to view your downloaded videos. -When you don’t have an active Wi-Fi connection to connect your device, tap "Videos" to view your downloaded movies and TV Shows. -Please note that Prime Video content isn't available for download when your Fire tablet is connected to a 4G/WAN wireless network.
-To download videos, you'll need to connect your device to an active Wi-Fi network.
-The file size of your video depends on the duration of the movie or TV show you're downloading.
-You can find this information on the video's detail page before purchasing or downloading.