Though mine is still in process of being shipped, Match received their Kindle Fire devices today. I got to play with it a little and test some pages with it. I also needed its user agent string, which I couldn't find on the web. So here it is:
Mozilla/5.0 (Macintosh; U; Intel Mac OS X 10_6_3; en-us; Silk/1.1.0-80) AppleWebKit/533.16 (KHTML, like Gecko) Version/5.0 Safari/533.16 Silk-Accelerated=true
User agent strings tend to be full of lies anyway, but I expected a very Android-like user agent string. I was surprised to see the Macintosh-ness of it. Anyway, there is the first gen user agent string of the Kindle Fire if you are looking for it.
As for the device itself, I like it so far. I was surprised at the heaviness and the usability definitely needs some work in various areas. It was also frequently choppy so could use some more power. But still, it appears to be a nice device on first usage.

Tad
I was surprised at this myself. Personally I don't get why it is that they blatantly say something COMPLETELY different from what the device actually is. It's not like it will force compatibility with sites that are doing UA detection.
Also curious is the fact that if silk acceleration is turned on, the traffic will be coming from Amazon's servers, not from the network that the device is on.