In a large, deep skillet, heat 1 inch of oil over medium-high heat until it reaches 350 degrees on a deep-fry thermometer.
Meanwhile, in a bowl, combine the chicken, cheese, salsa and 1/2 tsp. salt.
Wrap tortillas in a towel; microwave until warm, about 1 minute. Spoon a scant 1/4 cup chicken filling onto 1 tortilla; roll up snugly. Repeat with remaining chicken filling and tortillas. Fry the flautas seam sides down, turning once, until golden, about 5 minutes; drain on paper towels.
In a bowl, whisk 1/3 cup sour cream with the lime juice; season with salt. Toss in the remaining ingredients. Serve the flautas with the salad and the remaining sour cream, for dipping.