Bring the soy sauce, maple syrup, red pepper flakes, 1/4 cup lemon juice and 1 cup water to a boil in a wide saucepan. Add the chicken in a single layer; reduce the heat to medium low. Cover and simmer, turning occasionally, until just cooked through, 10 to 15 minutes. Remove the chicken to a plate (reserve the liquid). Let cool, then shred.
Peel the sweet potatoes and cut into 1/2-inch cubes. Add to the liquid in the saucepan; cook over medium heat, stirring occasionally, until just tender, about 15 minutes. Transfer to a plate with a slotted spoon (reserve the liquid). Let the potatoes and liquid cool.
Cut the apples into matchsticks. Peel the cucumber, cut in half lengthwise and thinly slice. Combine the apples, cucumber, kale, sesame seeds, chicken, sweet potatoes and sesame oil in a large bowl. Toss with the reserved cooking liquid and the remaining 2 tablespoons lemon juice. Season with salt and pepper; sprinkle with the peanuts.