Place the chicken breasts, taco seasoning, diced green chiles, and salsa into the slow cooker.
Cook on high for 2–3 hours, or until the chicken reaches 165°F (74°C) and is fully cooked.
Remove the chicken from the slow cooker and shred it with two forks; return shredded chicken to the cooker and stir in mayonnaise until combined.
Heat a large skillet over medium–low heat and warm one flour tortilla briefly in the pan.
Sprinkle about 1/4 cup shredded cheese evenly over the tortilla.
Spoon about 1/2 cup of the shredded chicken mixture over the cheese.
Top the chicken with another 1/4 cup shredded cheese, then place a second tortilla on top and press gently to compact.
Cook 2–3 minutes until the bottom tortilla is golden brown, press once more, then carefully flip with a spatula and cook another 2–3 minutes until the second side is browned and cheese is melted.
Remove from the pan, cut each quesadilla into four triangles, and serve hot with shredded lettuce, diced green onion, sour cream, and taco or hot sauce as desired.