I am not sure if this will answer it, but I was having the same problem with a recent Kindle book purchase as far as getting it on to my Kindle, the device is full message. I tried removing some things, without result, I also unclicked an option that involved default downloads to my SD card, which was nearly full.
Something that DID work for me was to go to my account on computer and go to digital purchases. It listed my digital books purchased. I clicked on Actions and chose something where I hooked up my Kindle to my computer by USB "Download & transfer via USB" I selected my device. Then "Transfer Tip: After downloading, use your USB cable to connect your computer and Kindle. Your Kindle will appear as a drive on your computer. Copy your downloaded file from your computer to your Kindle's documents folder." And then, I am not sure I remember exactly what I did next . . . it may be that the file appeared in Kindle on my device. Anyways, this route worked for me.