Fill a large saucepan with about ¾ inch oil. Heat over medium heat to 375°F.
In a medium bowl, combine chicken, cheese, salsa, diced chiles, garlic salt, and pepper.
Working with 4 tortillas at a time, spread a heaping spoonful of chicken filling along the middle of each tortilla. Roll the tortillas tightly around the filling and secure each one with a toothpick.
Using tongs, hold each flauta in hot oil until firm, then release to continue cooking. Cook until golden brown, about 2 minutes, then remove to a paper towel–lined plate and immediately season with salt.
Transfer flautas to a foil-lined baking sheet and keep warm in the oven while assembling and cooking the remaining tortillas. Serve warm with toppings.