Stir orange juice, soy sauce, garlic, orange zest, ground ginger, and red pepper flakes together in a bowl until thoroughly combined.

Heat oil in a large skillet or wok over medium-high heat. Cook and stir chicken and orange juice mixture in the hot oil until the chicken is no longer pink in the middle and the juices run clear, 7 to 10 minutes.

Whisk chicken broth and cornstarch together in a small bowl; stir into the chicken and sauce mixture in small amounts until sauce has thickened to your liking.

Mix stir-fry vegetables, sugar snap peas, broccoli, and carrot into the chicken and sauce mixture; cook and stir until the vegetables are slightly softened, another 7 to 10 minutes.