Coat a large nonstick skillet with cooking spray. Add eggs and cook over medium heat until set, about 2 minutes; remove to a plate. Cut into strips.
Wipe out skillet. Prepare rice mix in skillet following package directions, about 20 minutes. During the last 7 minutes of cooking time, add chicken, vegetables, bamboo shoots and soy sauce. Stir in egg and cook, covered, for remaining 7 minutes.
Stir in sesame oil and scallions. Let stand, covered, 5 minutes.