You can't read a kindle book on a nook. I have a nook and love it but if you aren't interested in buying into the technology then I suggest you just download the free kindle app that works on pretty much any smart phone, iPad or even your computer I believe so you can read your brother's book.
Btw, the technology is the same behind the kindle and nook. The difference is that kindle uses amazon's proprietary file type and nook uses ePub that is more and more becoming the standard because it can be used across platforms. I love my nook and never leave home without it. I borrow library books to read on it and buy from barns and Nobel as well as other online ebook stores. I know there are just s many happy kindle owners out there. Once you start using an ereader it doesn't take long to start wondering why you waited so long.
I pedal for chocolate
1999 Klein Quantum - Terry butterfly Ti
2011 Trek Utopia - Bontrager Nebula Plus...for now