Preheat the oven to 375°F (190°C).
In a skillet, heat the vegetable oil and sauté the chopped onion and minced garlic until they are soft and fragrant.
Add the shredded chicken to the skillet and season with cumin, chili powder, salt, and pepper. Cook for a few minutes until the chicken is heated through and well-coated with the seasonings.
Pour a small amount of the red enchilada sauce into the bottom of a baking dish to coat it.
Place a spoonful of the chicken mixture onto each flour tortilla, sprinkle some shredded Monterey Jack cheese on top, and roll up the tortillas. Place them seam side down in the baking dish.
Once all the tortillas are rolled up, pour the remaining red enchilada sauce over the top of the enchiladas and sprinkle with the remaining shredded cheese.
Cover the baking dish with foil and bake in the preheated oven for about 20-25 minutes, or until the cheese is melted and bubbly.
Remove the foil and bake for an additional 5-10 minutes to allow the cheese to slightly brown.
Garnish with chopped cilantro and serve hot with a dollop of sour cream on top.