Files comes as a system app on our Droid 3s. This is probably why it won't install on your Fire or like you said because of graphical..etc.
If you have your device rooted, you could try to place the FileManager.apk in the system\app folder and set the permissions to Owner: Read/Write, Group: Read, and Others: Read. (You can do this using ADB as well) and reboot. This should install the app.
However I would suggest just trying ES File Explorer instead, it should be compatible with your kindle. Good luck
Droid 1 - ChevyNo1 SS 5.6 1.0Ghz LV Kernel (retired)
Droid 3 - Gummy ICS 4.0.4 Modified Build 1.2.x built from source