Heat walnuts in a dry skillet over medium-high heat 1 to 2 minutes until walnuts are slightly toasted. Set aside and reserve.
Coat a 12-inch nonstick skillet with vegetable cooking spray and set over medium-high heat. Add onion and sauté, stirring occasionally, 3 minutes. Add chicken and sauté, stirring occasionally, until chicken is golden brown and cooked throughout, about 6 minutes. Stir in broccoli, carrots, snow peas, sauce and walnuts; heat through.
To assemble, place tortillas on work surface. Cover with rice, dividing equally, leaving a 1-inch border empty on each tortilla. Top with chicken mixture, dividing equally. Beginning at the bottom of each tortilla, roll the bottom over the filling, then fold in the sides, and lastly, roll the bottom over the filling to enclose the package.