What comes with the Kindle Fire is an email app that can work with whatever email address you have (including @gmail).It's not the only email app for Android out there, though. Others include Aqua, K-9, Kaiten, and so on.All Your Personal Email
The new email app on Kindle Fire HD makes sending mail, viewing attachments, and syncing contacts simple. With full support for the world's most popular email providers - including AOL, Exchange, Gmail, Hotmail, Yahoo!, and more - it's our easiest-to-use email ever.
Those others may be availabe in the Amazon app store; I'm not sure.
The email app I prefer is Gmail — not just Gmail the email service, but Gmail the actual app that I use to access the email service. Since it's made by Google, it's not available in the Amazon App store, and it's not even installable by sideloading without jumping through a few other hoops first (if I remember correctly).
Some apps are available from the Google Play store, but are not available from the Amazon App store. I do not think the reverse is true. So depending on exactly which apps you want to use, you may find the Kindle Fire to be a bit limiting, or you may find that it doesn't matter because the stuff that's not easily available isn't stuff you'd want to use anyway.
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