Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking dish.

Heat a large skillet over medium-high heat. Cook and stir beef, onion, and green chiles in the hot skillet until beef is browned and crumbly, 5 to 7 minutes; drain and discard grease.

Add water, chili powder, salt, red pepper flakes, cumin, and garlic powder to beef mixture; bring to a boil. Reduce heat to medium-low and simmer. Stir in refried beans; cook until heated through, about 5 minutes.

Mix cream of mushroom soup and sour cream together in a bowl.

Fill each tortilla with beef mixture and roll tortilla around filling. Arrange burritos in the prepared baking dish; top with sour cream mixture.

Bake in the preheated oven for 20 minutes. Cover burritos with Cheddar-Monterey Jack cheese blend. Bake until cheese is melted, about 10 minutes more.