So I rooted my fire using Burrito Root.
The SuperUser app was available once that was complete. I got a version of Google Services Framework from http://code.google.com/p/androidmarketu/downloads/list
When I try to install the Google Services Framework, it tries to install it but then it says "Not Installed".
I have the Allow Other Applications set to ON.
I don't wish to change the stock ROM. All I need is the Google Talk application to work on the Kindle Fire.
adbconfigured on your computer you can use it to get a more detailed error message about why the install is failing (if you want). You'd do this by downloading the .apk file to your computer, plugging in your Kindle, and then runningadb install /path/to/apk. – eldarerathis♦ Jan 10 '12 at 14:37