A quick search for the Nook app in the Kindle Fire's Appstore results in absolutely nothing.
The Nook app is available for Android (which is the Fire's OS), but Amazon chose to exclude its competitor's e-reader app from its store.
We don't blame it, but those who are making the switch from Nook to Kindle (or use both) would benefit from access to their old purchases.
After all, it's not like you can sell your old Nook purchases to a used bookstore, right?
Follow the steps to reclaim your Barnes & Noble Nook books and access them on your new device:
Step 1: Go to the Kindle Fire's settings (upper-right) and tap "More," then "Device." Turn "Allow Installation of Applications" to "on." You'll get a warning--just tap "OK."
Step 2: Launch your Fire's browser and head to m.getjar.com. GetJar is one of the best places to get third-party Android apps. At the top of the page, search for "Nook." When you find it, tap Download. You'll be asked to download the GetJar app. Tap "Download GetJar."
Step 3: When the download completes, tap the file in the downloads list (which you can access from your Kindle's top bar), and select "Install."
Step 4: Once GetJar installs, find it in your Fire's app library, open it, and search for "Nook" again. Tap "Download," review the app's permissions, and tap "Install." The Nook app will show up in your Kindle Fire's library.
Head back to the GetJar app anytime you want to download other third-party apps like Google Maps, Dropbox, Facebook, or a different browser like Dolphin HD. None of these apps is available in Amazon's Appstore, but you can download them from GetJar.