Whisk together mayonnaise, sweet chili sauce, Sriracha, honey, and rice vinegar in a medium bowl until smooth.
Place the cooked shredded chicken in a large mixing bowl and pour the sauce over it; toss until thoroughly coated.
Divide the cooked rice evenly among four meal prep containers.
Top each rice portion with a quarter of the bang bang chicken mixture.
Arrange the cucumber slices and steamed edamame next to the chicken in each container.
Garnish with sliced green onions and toasted sesame seeds.
Seal containers and refrigerate for up to 4 days for meal prep utility.