In a large mixing bowl, combine the shredded rotisserie chicken, shredded Pepper Jack cheese, black beans, and salsa. Mix everything together until well incorporated.
Lay a tortilla flat on a clean surface. Spoon about 2-3 tablespoons of the chicken and black bean filling onto the lower third of the tortilla. Tightly roll the tortilla around the filling, tucking in the sides as you go to secure the contents.
Heat a non-stick skillet over medium heat and add enough oil to cover the bottom of the pan. Fry the flautas seam-side down for about 3-4 minutes on each side until golden brown and crispy.
For baking, preheat your oven to 400°F (200°C). Place the flautas seam-side down on a baking sheet lined with parchment paper, brush the tops with oil, and bake for 15-20 minutes until golden brown.
In a small bowl, mix together the sour cream, adobo sauce, and lime juice. Adjust seasoning to taste.
Arrange the crispy Chicken and Black Bean Flautas on a serving platter and serve with the creamy dipping sauce.
