This isn't a Tndeer issue but an Android/Photobucket not getting along problem. Photobucket know's about it and are hopefully working to get it fixed.
To get around it until then, Firefox for Android
and Chrome for Android
both work fine and show the missing images, so I suggest installing and using one of them until then.
The Kindle Fire is Android based so thats why the problem is there too, I don't have one so I don't know if you can download Android Play apps or what other browser options you have.