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You don't need to update your Kindle Fire. Kindle Fires are not affected by the requirement. Only regular Kindles are required to the update and 90% of the times, these updates are done automatically.
Set aside your Kindle fire. You don't need to worry about it. You need to check whether your regular Kindle is on latest update or not.
Go to this website and identify your Kindle from this website --> http://www.oberondesign.com/pages/identify-your-kindle-model
Once you identified the model, go to this website--> https://www.amazon.com/gp/help/customer/display.html?ie=UTF8&nodeId=201994710
You can determine the software version of your regular Kindle from the above website. If you are not on latest version, then you need to update it. Go to this website and follow the steps in there to update it --> http://www.amazon.com/gp/help/customer/display.html?nodeId=200529680
If you have any difficulty on following the steps above, please let me know.