In a large skillet, heat the olive oil over medium heat. Add the diced onion and finely chopped jalapeño. Sauté for about 3-5 minutes, or until the onion becomes translucent and fragrant.
Sprinkle in the kosher salt, chili powder, and ground cumin. Stir well to combine, allowing the spices to toast slightly for about a minute.
Add the shredded cooked chicken to the skillet, mixing thoroughly to coat the chicken in the spice mixture. Cook for an additional 2-3 minutes until the chicken is heated through. Remove from heat and set aside.
Warm the flour and corn tortillas in a dry skillet or microwave for a few seconds to make them pliable.
Place a spoonful of the chicken mixture in the center of each tortilla, followed by a sprinkle of shredded Monterey Jack cheese. Roll the tortilla tightly around the filling, securing it with a toothpick if necessary.
In the same skillet, heat the vegetable oil over medium-high heat. Once hot, carefully place a few flautas in the oil, seam side down. Fry for about 3-4 minutes, turning occasionally until golden brown and crispy. Remove from the oil and place on a plate lined with paper towels to drain excess oil.
Once all flautas are fried, drizzle lime juice over them and serve with salsa on the side. Enjoy your homemade Chicken Flautas!