Bryan Morris has a post about how he has set up Emacs using org-mode to implement a Kanban board. He uses table mode within org-mode, and hyper-linking to link items within the table, to actual org-mode tasks. To me, this setup seems a little clunky, so I thought I'd describe my current system.
To me, the central point of Kanban is to keep the Work-in-Progress queue small to optimize your state of flow. I have a "backlog.org" org-mode file in which I keep track of all my tasks, large or small. Any new tasks go in here.
I have a keystroke set up in Emacs that will open my to-do file for the day. All to-do files live in a common directory, are named "YYYYMMDD.todo", and are opened in org-mode. From my backlog file, I transfer a small number of items to my daily to-do file (usually 2 or 3). I then concentrate on these items until they are complete. Only when they are all marked as DONE, CANCELLED or WAITING do I move another couple of items to the daily to-do list.
I also try and time-box throughout the day as rigorously as I can. To do this, I use the Due app on my iPhone. This system has been working really well for me.