Hi there! My name is***** am a computer professional with over 15 years of experience with both Mac and Windows computers, phones, tablets, and printers. It would be my pleasure to assist you with this. If you are actively using your Kindle Fire and it is is registered to your Amazon account, you can find the model number by going to http://www.amazon.com/myk and logging in with your Amazon account info. After you have logged in, please click on the Device tab. Your Kindle will be shown there along with the model number and the serial number.
If you have not yet registered your Kindle, you may be able to identify by going to this website:
Please give this a try and let me know the results.