Make the dressing by combining mayonnaise, lemon juice, Dijon mustard, onion powder, celery seed, and salt to taste in a small bowl; whisk until smooth.
Dice leftover chicken into roughly 1/2-inch cubes until you have about 4 cups.
Place the diced chicken in a large bowl and toss with some of the dressing to lightly coat; let it marinate while you prepare the vegetables.
Thinly slice the red and green cabbage (use a mandoline or a sharp knife), then chop the sliced cabbage into shorter, bite-sized lengths.
Thinly slice the green onions.
Add the red cabbage, green cabbage, and green onions to the bowl with the marinated chicken; add the remaining dressing to taste.
Toss everything together until evenly coated, then season to taste with salt and fresh-ground black pepper and serve.