Bring 1 ¼ cups broth, rice, beans, 1 ½ teaspoons chili powder, and ½ teaspoon salt to boil in medium saucepan over medium-high heat. Cover, reduce heat to low, and cook until rice is tender and broth is absorbed, about 20 minutes. Remove rice from heat and let sit, covered, for 10 minutes. Add scallions and fluff with fork to incorporate; cover to keep warm.
Meanwhile, cook oil, garlic, and remaining 3 tablespoons chili powder in large saucepan over medium-high heat until fragrant, 1 to 2 minutes. Stir in tomato sauce and remaining 1 cup broth and bring to simmer. Nestle chicken into sauce. Cover, reduce heat to medium-low, and cook until chicken registers 160 degrees F, 10 to 15 minutes, flipping halfway through cooking.
Transfer chicken to cutting board and let cool slightly. Using 2 forks, shred chicken into bite-size pieces. Toss chicken with ¼ cup sauce and 2 tablespoons cilantro in bowl. Set remaining sauce aside.
Adjust oven rack to middle position and heat oven to 450°F. Line baking sheet with aluminum foil. Wrap tortillas in damp dish towel and microwave until warm and pliable, about 1 minute. Lay warm tortillas on counter. Mound rice in center of tortillas, close to bottom edge, then top with chicken, avocado, and Monterey Jack. Working with 1 tortilla at a time, fold sides then bottom of tortilla over filling, pulling back on it firmly to tighten it around filling, then continue to roll tightly over burrito. (Burritos can be held at room temperature for up to 1 hour before baking.) Place burritos seam side down on prepared sheet, cover tightly with foil, and bake until hot throughout, 20 to 30 minutes.
Before serving, whisk salsa and 2 tablespoons cilantro together in bowl, cover, and microwave until hot, about 1 minute (if you’re using homemade tomatilla salsa with fresh cilantro in it, no need to stir in extra cilantro at this point). Reheat red sauce in saucepan over medium heat until hot, about 3 minutes, adding water as needed to loosen consistency.
Arrange burritos on individual plates. Pour tomatillo sauce over half of each burrito and pour red sauce over other half of burrito. Drizzle with crema, sprinkle with remaining 2 tablespoons cilantro, and serve.