As a linux user myself, I've always been fairly happy with OverDrive.
As AnemicOak said, OverDrive to Kindle is handled via a redemption link which sends you to
http://amazon.com to add the checkout to your Kindle account, and you can then download it directly via your Kindle.
In fact, I sometimes checkout a book using the Kindle's Experimental Browser, redeem it, then exit the browser and download the book from my Cloud items... all without going near the computer!
(Note: this is only to show what
can be done. The E-Ink Kindle is not very powerful and the browser is "experimental" for a reason. But it works in a pinch.)
...
If you want to checkout EPUB books to use with a Kobo, then Adobe Digital Editions is available on Linux using winetricks. It is pretty stable and works well (in the sense that it successfully runs and is fully functional, although I happen to despise Adobe software and much prefer the Kindle checkout if possible).