Place chicken in a large skillet. Add chicken broth and cumin. Bring to a boil, cover and reduce heat. Simmer until chicken is fully cooked, about 20 to 30 minutes. Remove chicken and set aside. Shred once cool enough to handle.
Meanwhile, stir flour and water together. Slowly whisk into the skillet. Bring chicken stock back to a boil and boil about 5 minutes, until thickened. Stir chilies into the liquid then stir the shredded back in. Cool.
Assemble the enchiladas assembly line style. Start with the rice slightly off center of each tortilla. Top rice with chicken mixture, then beans, then corn and finally some shredded cheese.
Tightly roll up the tortillas and place in a 13×9 casserole dish. Pour the enchilada sauce on top and sprinkle on any remaining shredded cheese.
Refrigerate until dinner time or bake immediately at 350 degrees for about 15 minutes, until heated through.
