I have ES and Astro on my Fire, but FX
should work fine I would think. You'd just need to get the APK (easy using
APK Downloader or other methods) and enable unknown sources in order to sideload it. Or sideload the Google Apps and use the Play store directly from the Fire (you'd have to do this if you want to try and use the paid Plus add on for FX).
EDIT: According to the FX dev thread on XDA you can also get the APK from the archive here...
http://android.nextapp.com/fx/