Rinse the jasmine rice under cold water until the water runs clear. In a medium saucepan, combine the rinsed rice and water. Bring to a boil, then reduce heat to low, cover, and simmer for 15 minutes or until the rice is tender and water is absorbed. Remove from heat and let it sit covered for 5 minutes. Fluff with a fork before serving.
While the rice is cooking, prepare the sticky chicken. In a large bowl, whisk together the soy sauce, honey, rice vinegar, sesame oil, minced garlic, grated ginger, and red pepper flakes (if using).
Cut the chicken thighs into bite-sized pieces and add them to the marinade. Let the chicken marinate for at least 15 minutes, or up to 1 hour in the refrigerator for more flavor.
Heat a large skillet over medium-high heat. Add the marinated chicken (reserve the marinade) and cook for about 5-7 minutes, stirring occasionally, until the chicken is cooked through and browned.
Add the reserved marinade to the skillet and bring to a simmer. Cook for an additional 3-5 minutes, allowing the sauce to thicken and coat the chicken.
In the last few minutes of cooking, add the broccoli florets and sliced bell peppers to the skillet. Stir until the vegetables are tender but still crisp.
To serve, divide the cooked rice among bowls, top with the sticky chicken and vegetable mixture, and garnish with sliced green onions and sesame seeds.