Preheat the oven to 375 degrees F (190 degrees C).
Warm the flour tortillas to make them pliable. Mix the rice and beans together and spread equally onto the center of each tortilla. Divide the meat equally on top of the bean mixture. Top with half the cheese.
Fold in the sides of the burrito and roll it tightly.
Pour half the enchilada sauce into an 8×8″ baking dish. Place the rolled burritos seam-side down in the baking dish. Pour the remaining sauce over the top. Bake for 10 minutes. Remove from oven and sprinkle on the remaining cheese. Continue cooking for 3-5 minutes, until the cheese is melted.