Heat the walnuts in a small skillet over medium-low heat. Cook until the walnuts are lightly toasted, about 3 minutes. Remove from the heat and let cool. Make the vinaigrette: In a medium bowl, whisk together the lemon zest, lemon juice, garlic, brown sugar, parsley, salt, and pepper. While whisking continuously, slowly drizzle in the oil until combined. In a large bowl, combine the kale, chicken, beans, and walnuts. Drizzle with the vinaigrette and toss to evenly coat.