Because Kindle is technically a competitor, I cannot advise you to modify or side load content on their device, because it may violate your warranty or EULA for the kindle device. 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, you should see it on the app menu.
Kindle Fire HD for AXIS360
Kindle Fire for AXIS360
3 Easy Steps