Because Kindle is technically a competitor, we cannot assist you to modify or side load content on their device, because the device may not have the required settings for proper application functionality. However, if someone wanted to side load Blio, they could do so by making sure non market apps can be installed from the android settings > Applications menu. A file browser is also needed. ES File explorer is a good one that is available in the amazon market.
This is the file that you will need to open on the device
After you install the app, go to the home screen and select Apps > Device from the top menu bar and you will see the Blio app.
Another way to side load apps is to download a 3rd party app store like goodereader
Once the 3rd party store is installed, you can use it to find and download Blio. You can also use it to download Blio or Blio updates.
NOTE: Side loaded applications do not get automatic updates, so this is recommended for users to be able to get updates.