Unfortunately the new app does not support Kindle. See the following response to my inquiry regarding log in problems:
Thank you for contacting the library. I'm sorry you are having troubles with the app.
What type of device are you using? If you are using the website, Magic Wall, then please try checking out a book before registering. It seems counter-intuitive, but Axis 360 technical support has explained that this is the work around for getting registered on the site.
Also, please keep in mind that these eBooks are not available for the eReader Kindle Paperwhite. The Amazon eReaders were designed to only work with the Amazon store and this new system does not support the Amazon ebook format. I'm sorry for the inconvenience.
If you have a tablet or Kindle Fire, then you can download the app for an all-inclusive reading experience, or you can download the ePub format of a eBook for transfer to a device that supports that format.