Preheat the oven to 350 degrees. Toast the walnuts until crisp and fragrant, about 10 minutes. When cool enough to handle, chop coarsely; set aside.
In a large bowl, whisk together olive oil, flaxseed oil, vinegar, honey, and 2 tablespoons water; season to taste with salt and pepper.
Add apples, dried cranberries, celery, onion, and chicken; toss to combine. Divide among 4 plates; top with walnuts.