Cook rice according to package directions, omitting salt and oil. When rice is done, add rice vinegar and stir. Evenly spread rice on a sheet pan to cool.
Cut shrimp into 1-inch cubes. In a small bowl, combine cucumber and chives. In another small bowl, combine mayonnaise and sriracha sauce.
Using a 1 cup dry measuring cup, layer ¼ cup cucumber, then 2 tablespoon of avocado, then ¼ of the shrimp, and 1/3 cup rice.
Carefully turn the cup upside down to turn the stack out onto a plate, lightly tapping the bottom of the cup if necessary. Sprinkle with Furikake and drizzle with 1 teaspoon soy sauce and sriracha mayonnaise.