Kindle Fire ships with a debugging tool called the Dalvik Debug Monitor Server (DDMS). When you connect device with USB cable you can use ddms utility from Android SDK to take screenshots of device screen without rooting it. If you already have debugging environment set up all you need is to run this utility and take screenshot any time you want. If you do not have it read this article from Pigs, Gourds and Wikis blog.
Hopefully soon we can hear that somebody discovers how to make it on device without debugging it :-)