Kindle Fire Update:
I decided that while I liked the calendar feature on the Kindle, I didn't like the default mail program. So I thought I'd load the Google Mail app. The problem is it is not available on the Kindle App Store - only on Google's store.
However there are steps to bypass this and they were fairly simple. It is called side-loading and I found this article and it was even easier than it sounded:
In the steps to get the apps installed, they talk about using a file explorer and copying the apk files over, but the files I needed were linked at the bottom of the article, and all I had to do was click, download and install. Very simple.
I side-loaded the Gmail and Google+ apps for now. Both seem to work with no problems. I may try others in the future. I did keep the default calendar program and I like the way it works for now.
AndroidCowboy.com is a great website to get started on to find out how to use Android tablets and apps, in general, as well as some Kindle specific info.