Using a spiral vegetable slicer fitted with the small blade, cut zucchini and yellow squash into long strands (about 7 cups lightly packed strands). Keeping carrot separate, cut carrot into long strands (about 1 cup lightly packed strands). If desired, cut through strands with kitchen scissors to make them easier to serve.
In a bowl combine Alfredo sauce, pesto, and red pepper.
In an extra-large skillet heat oil over medium heat. Add mushrooms; cook and stir 4 minutes. Add carrot; cook and stir 1 minute. Add squash mixture; cook and toss with tongs 2 minutes. Stir in Alfredo mixture, chicken, tomatoes, and peas; heat. Sprinkle with basil.