With the HD/HD+ you have access to the Google Play Store and the Kindle app. The NT and NC don't have this, so no you can't read Kindle eBooks unless you root or strip DRM.
You can get an N2A card of the equivalent (or make one yourself) which will allow you to boot into Android if you choose. Then you can get the Kindle app and read Kindle books on yyour NC. That's what I've done. Not quite as convenient as having a Kindle app right on the Nook side, but it works.