Has anyone successfully transfered a CodeIgniter app to Kohana 3.x?
No, it'd be virtually impossible to just copy everything over.
You had a better chance with Kohana 2.3.4 as it was derived from CodeIgniter and was similar. Kohana 3 is a total rewrite so it would be like migrating to a new framework.
Have a look at Kohana Docs:
Although it is not specifically for Kohana 3 but probably you can get the idea from it.
I have migrated a CodeIgniter app over to Kohana 3.x, but things are very different so I wouldn't call it a direct port. About the only things I were able to reuse were views (although I converted them to mustache templates) and the SQL from the models.
There is no reason to switch frameworks for an existing application unless there will be continued work on it and you are familiar with the new framework. Because if you do switch, you will basically be rewriting the application. That said, I chose to do my app because I will be maintaining it for a long time and I am more familiar with Kohana. YMMV