[tomsem]

At least last time I checked, the Overdrive app will read side-loaded ePub but only if there is no DRM.

I cannot figure out how to sideload directly over USB. What worked for me was to put it in a folder on the Fire (say 'Download') then use ES File Explorer, navigate to the folder and tap on it. 'Open With' will come up and one of the programs should be Overdrive Media Console. OMC will then copy it to a folder that it manages and generate a thumbnail. Then you can delete it from the original location.

I tried copying it directly to the Overdrive folder but OMC doesn't seem to see it unless it is served up by 'Open With'.

I usually use Dropbox for this (having side loaded it from 'other sources') for this sort of thing. Then you don't have to hook up a cable, and use ES File explorer. Just download and tap to Open With. Or you can use the web browser, and login to your Dropbox account (or google drive etc.) and download it that way.