Shred and combine cheeses; toss with flour and set aside.
In a fondue pot, whisk together stout, cider and Dijon mustard; bring to a simmer.
Once liquid begins to bubble slightly around the edges, start adding cheese mixture to the pot stirring constantly until all cheese has been added and fondue is a smooth consistency. You may need to thin it out with more stout. Be careful the heat does not get too high; if you have an electric fondue pot keep at a simmer. If using a sterno, you may need to regulate the temperature with the snuffer.