They are stiff when new, plus flannel is thicker than regular cotton, plus the rag die is the hardest die to run through because it has ***so*** many cutting edges on it. Try running just one layer through at a time until the machine loosens up. (I thought it was the rollers, but it makes sense that it's the new die!) Also, adding the paper as described by luvTooQuilt is a really, really good idea -- saves you a lot of time trying to pick threads out of the die later on.
When I first got mine, I started with the tumbler die and could cut only 2 layers at a time for the first couple of hours of use. Now I can cut 4 layers of fabric at a time with that die.