Yes, this is possible via Corona Enterprise. You would then have to set up the Android activity to use the “SYSTEM_UI_FLAG_HIDE_NAVIGATION” flag (API Level 14; Android OS 4.0) or the “SYSTEM_UI_FLAG_FULLSCREEN” flag (API Level 16; Android OS 4.1).
http://developer.android.com/reference/android/view/View.html#SYSTEM_UI_FLAG_HIDE_NAVIGATION
http://developer.android.com/reference/android/view/View.html#SYSTEM_UI_FLAG_FULLSCREEN
The “SYSTEM_UI_FLAG_HIDE_NAVIGATION” will display the activity fullscreen until the end-user taps on the screen. Then Android will automatically display the navigation bar at the bottom again, which will also cause your app to be resized in the vertical direction. The “SYSTEM_UI_FLAG_FULLSCREEN” flag always shows the activity in fullscreen, even when the end-user taps on your app.
That said, I have no idea if Kindle Fire devices will respect these flags. They use a fork of the Android OS and do not follow all of the rules documented by Google.