If you're looking to use Firefox on the Kindle Fire, where it is rather difficult to access third-party web browser apps, it is possible to install Firefox 9 Aurora from the Mozilla Wiki.
Since the Kindle Fire doesn't let you download web browser apps from the Android marketplace, even after you have enabled third-party application downloads, open up the Silk browser and go to the Mozilla Wiki site. Scroll down to "Download Aurora" to install Firefox 9.
If you try to download the app for from the Firefox site and Android Market, you'll see a notification stating, "Could not find that app in the Amazon Appstore for Android at this time."
Aurora, which Firefox first announced in April, is a release channel designed to deliver experimental builds of the browser faster to users. Other Firefox channels include Nightly, which is highly unstable, and Beta, which is fairly stable.
While it's not easy to install browsers like Google's Chrome to Phone Android app, Dolphin, Skyfire and Opera on the Fire, you can sideload those apps onto your device by connecting your Kindle to a computer and syncing it via a USB connection. Read directions on how to do this here, but keep in mind that it is not easy and could also void your warranty.
We would love to be able to have more easily accessible options for browsers on the Kindle, but it seems that Amazon is adamant on people using Silk. Silk, which is a cloud-accelerated web browser powered by Amazon Web Services, is exclusively available on the Kindle Fire.
"Amazon isn't a normal version of Android for a reason," Fairmort programmer Damien O'Neill writes on Google+. "They want to control the experience a lot more than would typically be allowed and funnel customers through their own store, not just for media but for applications as well. Much more like Apple. I think it would concern Google to be honest."
Click Download Aurora to directly download the browser to your device.