Q: Can I add Axis 360 to my Kindle without downloading from Amazon's Appstore?
Yes, there is a way to bypass the Amazon Appstore and download and install Axis360 to your Kindle.
Please note that future updates will not be automatically installed if you choose to use this method.
Why would anyone want to use this method, then?
Sometimes, updates are created to correct bugs in the software. Updates must be approved by Amazon before they are made available to download from their Appstore - sometimes the approval can take a while, and you might need to get an ebook and read it before that happens.
Here is walk-through of how to install Axis 360 without using Amazon Appstore: Axis 360 Sideloading Workaround.
If you need to check whether your Kindle is compatible with Axis 360, check out the Kindle Fire Compatibility Matrix.