Heat oil in large saucepan over medium-high heat. Add peppers and onion; stir-fry about 5 minutes.
Add chicken broth, vegetable stock, and soy sauce. Bring to boiling. Lower heat; simmer for about 5 minutes.
Stir together vinegar, red pepper flakes, salt, pepper, cornstarch, water, and sesame oil in a small bowl until smooth. Add to soup with fresh snow peas (if using); cook for about 5 minutes or until thickened and bubbly.
Add tofu, frozen snow peas (if using), and water chestnuts. Gently heat through.