Heat a large skillet over medium-high heat. Cook and stir beef and onion in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Add chili and salsa and mix well.
Fill tortillas with 1/2 of the beef mixture and roll tortilla around the filling forming burritos. Mix the remaining beef mixture with cream of chicken soup and sour cream. Cover the bottom of two 9x13-inch baking dishes with soup-beef mixture. Arrange burritos in the baking dishes; top with remaining soup-beef mixture. Sprinkle Cheddar cheese over burritos. Cover dish with aluminum foil.
Bake in the preheated oven until cooked through and cheese is bubbling, 40 to 45 minutes.