You can read your (ePub and Google) eBooks on the Kindle Fire.
The Kindle Fire is based on Google's Android operating system, and IndieCommerce has worked with Bluefire to create the IndieBound Reader app for Android devices.
The answer is that it is in fact possible to run the IndieBound Reader app on the Kindle Fire through a process called sideloading. Sideloading refers to the practice of installing apps without going through the official app store on a device.
There are many great sideloading walkthroughs for the Kindle Fire online listed, with some listed here:
An APK file (described in the tutorials above) for IndieBound Reader can be downloaded directly from http://www.indiebound.org/reader.
Please note: IndieBound Reader was not specifically developed to run on the Kindle Fire. However, the app has been tested with good results on this device.
Also, customers should consult Amazon's Terms of Service before attempting to sideload apps. As of 12/22/2011, there was nothing in these Terms of Service precluding this practice, but users should check in case Amazon's terms have changed.