Whether you can read it on a Kobo depends on whether it's DRM'd, and Amazon doesn't provide that info. (They're really big on "you can read it on any device that works with our program! And that's all that's important!")

Some of the free ebooks (maybe many of them? because the agency publishers aren't participating?) released as part of the library program are not DRM'd; the only hassle is sorting out how to get the book from Amazon to a device that Amazon doesn't approve of. That, I can't help with; I know it'd involve installing the Kindle-for-PC program to download the file, and I've got no idea where those get saved on the hard drive.

If it's got DRM, you'd need a script that strips the DRM before it can be read on a different device; that's where the Apprentice Alf blog comes in.