Amazon Kindle does not directly support ePub files but DRM-free PDFs can be read on a Kindle.
There are some indirect ways you can make your ePub files readable on a Kindle. If you are interested you can visit the Kindle Knowledge base on Amazon and search for side loading or ePub. One approach involves sideloading 3rd part apps like Nook (for android).
You can also use the Kindle Cloud Reader.
The Overdrive App works on many (4th generation or newer) Kindle devices. Below are instructions on how to download it. Please note you will also need an Adobe ID to authorize your device.
On your Kindle go to the App Store for your Kindle device (Minimum Operating System Android 4.0) and download the Overdrive App--it's called Overdrive Media Console.
2. Open it and you will have to authorize it with your Adobe Digital Editions username and password. (The Adobe ID mentioned above)
3. Search and add whatever library it is you use for eBooks in the 'Add Library' page--it will come onto your Overdrive looking like an app itself.
4. Tap it to open it, and you'll be 'in' it just like you were online, log in, etc, search for books, check them out, same as always, except now it'll down load straight into your Overdrive app.
Please contact Amazon or consult your device instructions for further assistance.