Now that the latest update has been pushed, is there a way to install Swype on the Kindle Fire without rooting it?
Still no way without root. (
But I'll post some quick links for root users.
The old method (need to edit settings.db with SQLite Database Browser): http://blog.pathany.com/2011/12/swype-on-kindle-fire.html
New easier methods:
With Kindle Fire Utility it's rather easy to obtain and revert root.