I hit Amazon up with a phone call, email, and Tweet. They haven't gotten back to me, so I took a stab at figuring it out myself. 

One thing to remember is that while Apple (AAPL) faithfully reports iPad sales numbers each quarter, Amazon does not do the same for the Kindle Fire. That makes this exercise a little bit tough. 

I took a look at estimates from IDC, which help out quite a bit. During Q4 of 2011 (when the Kindle Fire debuted), Amazon sold 4.8 million units, enough to take 16.8% of the global tablet market. In Q1, IDC reported that Amazon's market share fell to just over 4%, which implies sales of about 700,000. For Q2, sales were 1.25 million, for about 5% of the global market.

Using my own brand of magic seventh-grade math, I figured out that during the three quarters for which we have Kindle Fire sales estimates, it had 9.6% of the global market. Note, however, that this number does not include July or August, for which there are no numbers.

Now remember this: The Kindle Fire was a U.S.-only product. Therefore, its global market share will be significantly lower than its U.S. market share. It is reasonable to assume that U.S. market share was significantly higher than 9.6%, putting that 22% number within reach.

Comscore (SCOR) said in April that the Kindle Fire had more than half the U.S. Android market, which is probably enough to get to a 22% total market share number, if we assume that Android market share was about 40% of the U.S. market during this time period.

So I'll have to put my pitchfork down -- for now it looks like Amazon is telling the truth. 

Enough about the past, let's look towards the future. Amazon is holding a press event on Sept. 6, and in all likelihood, it's going to introduce the next edition of the Kindle Fire. However, that model will likely face an uphill battle in the marketplace.

Google's Nexus 7, released in July, makes for an awfully tough competitor in the bargain-bin category in which the Kindle Fire competes. It is extremely well-outfitted for its $199 price and very well reviewed. Google even pushed the Nexus 7 on Google.com in recent days, the same way Amazon pushes the Kindle family on Amazon.com.

And of course, if the mythical iPad Mini ever comes out (I have my doubts), all bets are off for low-priced tablets like Google's and Amazon's.

As for the Microsoft (MSFT) Surface tablet, it likely won't impact the Kindle Fire 2 unless it hits the widely-rumored-but-u​nlikely $199 price point. (Microsoft owns and publishes Top Stocks, an MSN Money site.)

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