In a large bowl, combine chicken, chiles, cheeses, salt, and hot sauce (if using).
Lay 1 tortilla down on a work surface. Spread a heaping ¼ cup of the chicken mixture onto the bottom third of the tortilla. Roll up tightly and place seam side down on a plate. Repeat with remaining tortillas and filling.
In a 10” skillet, heat oil over medium-high heat until the temperature reaches between 350-375 ° F. (You want to hear a sizzle as soon as the food hits the oil.)
Add 3 of the flautas to the oil, seam side down. Cook, turning every 30 to 60 seconds, until golden all over, about 2 to 3 minutes. Transfer flautas to a large paper towel-lined plate or baking sheet. Repeat with remaining flautas. Serve immediately with pico de gallo, sour cream, and guacamole.