In a large skillet, heat the olive oil over medium heat. Add the diced onion and jalapeño, cooking until the onion is translucent and softened, about 3-4 minutes. Stir in the kosher salt, chili powder, and ground cumin, cooking for an additional minute until the spices are fragrant.
In a mixing bowl, combine the sautéed onion and jalapeño mixture with the shredded cooked chicken, salsa, lime juice, and shredded Monterey Jack cheese. Mix well until all the ingredients are evenly combined.
Warm the flour and corn tortillas in a microwave or on a skillet until they are pliable. Place about 2 tablespoons of the chicken filling in the center of each tortilla. Roll the tortilla tightly around the filling and secure it with a toothpick if necessary.
In the large skillet, heat the vegetable oil over medium-high heat. Once the oil is hot, carefully add the filled tortillas seam side down in batches. Fry for about 2-3 minutes on each side or until they are golden brown and crispy. Remove the flautas from the oil and place them on a plate lined with paper towels to drain excess oil.
Serve the Chicken Flautas hot, accompanied by additional salsa, sour cream, or guacamole for dipping. Enjoy the crispy, flavorful goodness with your loved ones!