As you probably know, Amazon has made a number of sacrifices to make the price of its Kindle Fire tablet very competitive. This includes smaller screen, lack of navigation and volume buttons, no camera, no microphone, Bluetooth, GPS, etc. You can read more about this in my recent post about the Missing Features of the Kindle Fire, however, I thought there might be a slight chance for voice telephony when using a set of headphones with a microphone (such as those of the iPhone or an Android smartphone), but nobody got Skype to work with it yet, and who knows when and whether it will ever work(see Amazon Kindle Customer Forum Discussion about this)
In addition to the Amazon discussion forums, an article about adding the microphone functionality to the Kindle fire via a headset on Liliputing.com has several comments of users who tried to get Skype to work this way and so far it failed for everyone.
Therefore, the answer is no, at least not for now until Skype is customized for the Kindle Fire. As of January 5, 2012, Skype app is not available for the Kindle Fire on the Amazon App market. As you can see from the picture, search for Skype returned some messaging apps, Netflix and Pandora and some other irrelevant apps.
Skype doesn’t even seem to work (yet) on the Nook Tablet, the main competitor of the Kindle Fire. Even though the Nook Tablet has a built-in microphone (no camera though), Skype still doesn’t recognize it, so it currently can only be used for text chat.
One would hope that there are other ways of connecting a mic and a camera to a tablet, but lack of any ports and lack of Bluetooth is another obstacle that takes flexibility and extra options out of the equation for the Kindle Fire.