The eBook format compatible with the Kindle eReaders and apps is .mobi (Amazon's proprietary format). the ePub, ebook's standard formats, isn't compatible with Kindle devices.
A lot of books are already available in .mobi on StreetLib Stores (about 60 thousand) and you can use the format filter on the left to see them all and get the selection of book you'll immediately be able to read on your Kindle.
It allows you to open the .mobi file, and transfer it to any Kindle by simply clicking on the "Send to Device" button when the device is plugged in;
- Amazon's Send to Kindle:
Once installed, just register with your Kindle account, select the file to be sent to the Kindle and confirm.
Next, simply connect the Kindle to a Wi-Fi network and the content will be downloaded to the device.