Using Finestories .mobi Files with Kindle app on a Fire Tablet:
The easy way: Use the preferences panel in the Settings/My Account page to configure the Kindle downloads to be emailed to your kindle.
If you have reasons to use direct downloads (like not wanting to authorize kindle@Finestories or have it appear in your configuration, then you must side load or download the kindle files to your kindle via the browser.
Amazon makes it exceedingly difficult to use .mobi files with its kindle app on its fire tablets via direct download. If you download one of the books, the kindle app will put up an error message telling you that it’s locked using DRM and can’t be used and to get a proper copy from the Amazon Store.
The message is fake and Finestories’s files are perfectly useable with the Kindle app.
The second easy solution is download the EPUB version of the files, install a free EPUB reader on your Fire Tablet and use it to read the files.
However, if you need to use the Kindle app, maybe because you have multiple devices and like to sync location in books, then here is what you need to do:
1 - Download and install a file explorer app such ‘File Manager’ (free) from the Amazon app store.
2 - Download the ‘Kindle’ version of the ebook using your browser.
3 - Using the file explorer, find the book file in the Downloads folder and copy it.
4 - Go to the Books folder.
5 - Paste the file.
6 - The e-book should display in the Kindle app.
7 - If the book doesn’t show up automatically in the Kindle app, try turning your Kindle Fire off and back on.