As you would have already heard that Google has released its Flipboard competitor "Google Currents" in the United States recently. Similar to other Google applications, it is not available in the Amazon App Store, so you will need a workaround to install this application your Amazon Kindle Fire.
First you need root access on your Kindle Fire - You can find more on how to root the tablet here.
Now, you need to grab root explorer or any other file explorer from Amazon App Store that can give you access to system folder and make it writable.
Then you will need to download Kindle Fire APK from here.
Now, follow this guide to install Google Currents on your Kindle Fire.
Bonus: You can follow this tutorial to install Android Market on your Kindle Fire.