Kindle/Android Setup: MP3 Version
Here are the steps I used to successfully play the MP3 version of the audiobook on a Kindle Fire tablet (Fire OS 188.8.131.52). As far as I know, this same procedure will also work on an Android tablet or phone, but I had no way to test that to be sure. You may know of or find another method that works just as well or better. However you manage to accomplish it, the ultimate goal here is to get the MP3s downloaded and played in the VLC app.
VLC is a free, versatile player that can handle nearly every type of media. In terms of playing MP3s, I found that it works fairly well, displaying the artwork and allowing complete navigation of the audiobook's chapters. There are other players out there, but many of them are missing key features or are clunky and difficult to use. That includes the software that comes pre-installed with the Kindle (and presumably an Android).
Unfortunately, unlike my more detailed guide for downloading and setting up the MP3s in iOS, I can't provide screen captures in this one because something is wrong with my Kindle where it won't take screen caps. (It's supposed to, but it doesn't work for some reason.) Instead, I'll do my best to walk you through everything via text.
When you purchase the MP3s from this site, you'll be directed to a page with instructions on where to download a ZIP file containing them. This leads you to the audiobook's download page on the file hosting site MediaFire. You'll see a blue rectangular download button stating the ZIP's file name and file size; be sure to tap this and not one of the ads that MediaFire sometimes puts up that are made to look like download buttons but aren't.
Once the download is complete, the ZIP will be in your Download folder.
Next, open the VLC app. It should default to the Browse view; if not, select that tab at the bottom of the screen. There will be a list of folders, including Download, which you open by tapping it. Inside will be the ZIP that was downloaded from MediaFire. A good thing about VLC is that it can play the MP3s directly from the ZIP; there's no need for a separate app to unzip it. What's more, playing from the ZIP keeps the files together and in order (I didn't have much luck when I tried unzipping the MP3s and making a playlist).
Tap the ZIP file, and the audiobook will start playing via a mini-player at the bottom. Tap this, and it expands to the full player, showing the artwork and navigation controls. These include a scrubbing control (a horizontal line) for searching through a chapter, controls to skip forward or backward ten seconds, and left and right arrows that can either skip to another chapter or be held down to quickly scan within one. The table of contents can be brought up using the list icon menu in the upper right; tap it again to make it go away.
One thing I don't like about VLC is that once the MP3s are playing, there doesn't seem to be a way to close them, like if you wanted to stop and listen to something else in your Download folder. You can pause to stop playback, but the only way I've found to get back to the main screen is to close the app altogether (square icon at the bottom of the screen, then the X in the upper right of the app's window), then reopen VLC. This is also how to get to the Settings if you want to configure things: From the main screen, select More in the lower right, then Settings in the upper left.
And that's pretty much it. Enjoy listening.