There is no need - flash is already installed but with the last Fire firmware update, it disabled flash by default. When in your browser, choose menu-settings - and then under behavior click flash and choose always on.
Have been able to watch video content on web pages since getting my Kindle fire. However, in the past day or so (as of January 26, 2012) in the pane where the video should play I get a black screen and a notice that I need to update my Flash. How does one do this on Kindle Fire?