Yes, it is possible but will require “side-loading” the necessary app (Aldiko Book Reader Application). Once loaded, the Aldiko app works perfectly on the Kindle Fire (HD).
Step 1 Change a system setting on the Kindle Fire
On your Kindle Fire use the pull-down settings menu, choose “More” then “Device” then turn on the “Allow Installation of Applications from Unknown Sources” option.
Step 2 Download the APK file
Download the application “apk” installation file. The apk file can be downloaded directly from the source at the originators web site to your Kindle Fire. Open the web browser on your Fire and type in “Aldiko”. From the search results go to their Home page. Go to “Support” from the green menu bar.
On the Support page follow the first topic link (“Download the Latest…”).
On the Download page click the apk file link (“Aldiko Book Reader Free 2.2.3.apk” at the bottom of the page.
Download the file to a folder on your Kindle Fire.
Step 3 Install the APK package
Open a file manager app on your Kindle Fire, like ES File Explorer or Browser for SkyDrive (discussed in a previous posting and available from the Amazon App Store) and navigate to the folder where you put the apk file (usually “Downloads” by default). Touch the file name to launch the installation of the app.
Step 4 Get Books
Aldiko has a built-in Store for buying epub books, or get books from any source and copy them to your Kindle Fire by WiFi or USB cable. To add books to your Aldiko library use the “Files” widget on the main screen to specify epub files on your Kindle Fire. It is also capable of aquiring school and library books from the library’s “overdive” system without having to install a separate overdrive app. Enjoy!