Scoop the avocado into a blender. Add the sour cream and juice of 1/2 a lime and plush until smooth. Season with salt.
Squeeze the remaining 1/2 lime over the radishes in a small bowl and sprinkle with 1/4 teaspoon of salt. Toss the chicken with 3/4 cup of salsa in a medium bowl.
Wrap the tortillas in a paper towel and microwave until soft, about 45 seconds. Spoon chicken mixture down the middle of the tortillas. Fold the ends and roll up like a burrito; secure with toothpicks.
Heat 3/4 inch vegetable oil in a large skillet over medium-high heat until deep-fry thermometer registers 375 degrees. Fry the flautas, turning as needed, until golden brown, 2-3 minutes. Remove with tongs; drain on paper towels and remove toothpicks. Serve with avocado cream, radishes, cilantro, lime wedges and the remaining 3/4 cup salsa.