In a small bowl whisk together dressing ingredients. Halve radishes lengthwise and cut crosswise into 1/8-inch-thick slices. Diagonally cut scallions into 1/4-inch-thick slices. Discard coarse stems from watercress. In a bowl chill radishes, scallions, watercress, and bean sprouts while preparing chicken.
Pat chicken dry and season with salt. Cut chicken into 1/4-inch-thick strips, without removing skin. In a bowl stir together flour and cornstarch and add chicken, tossing until coated well. In a 12-inch skillet heat oil over moderately high heat until hot but not smoking and fry chicken in batches, separating pieces and turning them occasionally, until crisp and cooked through, 6 to 8 minutes. With a slotted spoon transfer chicken as fried to paper towels to drain.
In a bowl toss chicken with three fourths dressing. Toss vegetables with remaining dressing and combine with chicken.
