Skewer the jalapeños on a metal skewer or fork and roast over a flame until blackened, 3 minutes. Wrap in foil and let cool slightly. Rub off the skins and remove the seeds, then finely chop. Transfer the jalapeños to a bowl and add the chicken, cheese and cumin. Season with salt and pepper; toss well.
Wrap half of the tortillas in a towel and microwave at high power for 1 minute, until pliable. Arrange the tortillas on a surface and pack half of the chicken filling into cylinders across the bottoms. Tightly roll the tortillas around the filling, securing with toothpicks. Repeat to form the remaining flautas.
In a large skillet, heat 1/4 inch of oil. Line a baking sheet with paper towels. Fry half of the flautas over moderate heat, turning, until golden and crisp all over and heated through, about 4 minutes. Drain on paper towels. Fry the remaining flautas.
In a bowl, toss the radishes with the cilantro, onion and lime juice; season with salt and pepper. Remove the toothpicks and serve the flautas with the radish salad.