You can't read Kindle books on a Nook unless it is a Nook HD+ (the tablet that is running Android). Once you have the update with Google Play, you can add apps from the Google Play. This includes the Kindle app. Then you can read Kindle books on the Nook HD+.
Nooks read the EPUB format and Kindles read the Kindle format. I am not sure if the Kindle Fires can install the Nook app from their market. I haven't played with one.
You can read books from Gutenberg on your Nook.
http://www.gutenberg.org/ These are public domain books.
I am not sure about free books for Nooks. I will start looking for sources. I am usually busy with books from libraries on my Nook.