Place the chicken in a large bowl and season with cumin, oregano, salt, and pepper. Drizzle with olive oil and stir to combine.
Heat a skillet over medium-high heat. Add the seasoned chicken to the hot skillet and cook for 8-10 minutes, stirring occasionally until cooked through. Once cooked, remove from heat and set aside.
In a medium saucepan, combine the tomato sauce, vinegar, garlic cloves, chili powder, and sugar. Cook over low heat for 10 minutes. Once cooked through, remove from heat and set aside.
Preheat oven to 350°F (175°C). Take a tortilla and spread a spoonful of the sauce over one-half. Add some of the cooked chicken followed by some shredded cheese and fold over the other side of the tortilla to make a burrito. Repeat with remaining ingredients until all six are ready. Place the burritos in a greased baking dish, seam side down, and bake for 20 minutes until golden brown. While the burritos are baking, make the avocado ranch dressing by combining all ingredients in a food processor and blending until smooth. Serve with a burrito. For the cilantro lime rice, melt butter in a medium saucepan over medium heat. Add rice and cook for 2 minutes, stirring occasionally. : Add chicken broth, salt, cumin, black pepper and lime juice, and zest. Bring to a boil over high heat.
Reduce heat to low and simmer for 15 minutes or until all the liquid is absorbed. Remove from heat and stir in chopped cilantro. Serve with a side of burrito.