I am trying to clean up my library on my Kindle Fire. I can not figure out how to remove the title, not just the "Downloaded" version, from the "All" section of my list of books. The only way I can find is to delete the title from my Amazon.com account. Can this be done?
There are two sections in your library: your cloud/all tab and the downloaded tab. The downloaded tab shows what has been added to your device and is available to read immediately. Items from this tab can be deleted so they don't show up in the downloaded tab anymore.
The cloud/all tab (depending on model) shows everything which is available to you in your online library (including purchased, free, loaned, or Kindle Unlimited titles.) The only way to remove these from this tab is to delete them from your account. It isn't possible to hide them in the cloud library.
Deleting is not necessarily permanent - Kindle support can restore deleted purchases. It is not possible to restore them yourself, so if you've accidentally (or intentionally) deleted books from your cloud library just give them a call and let them know the title(s). This doesn't apply to titles deleted due to the original order being refunded.