Toss 3 Persian cucumbers, thinly sliced, ¼ cup unseasoned rice vinegar, and a big pinch of kosher salt in a medium bowl to combine. Let sit, tossing occasionally, until ready to use.
In a medium saucepan, bring 2 cups sushi rice or other short-grain rice, a pinch of salt, and 2½ cups water to a boil. Reduce the heat to low and cover with a tight-fitting lid. Cook until water is completely absorbed, and rice is tender,20–25 minutes; gently fluff rice with a fork.
Meanwhile, stir together 3 Tbsp. chili crisp, a drizzle of rice vinegar, and ⅓ cups plain Greek yogurt in a small bowl; set spicy yogurt aside.
Heat the broiler on high with a rack in the upper third of the oven. Pat 12 oz. salmon fillet, preferably skin-on, cut into 1"cubes, dry with paper towels, and place in a small bowl; season with salt. Add the remaining 3 Tbsp. plain Greek yogurt and a pinch of cayenne pepper; toss to coat. Arrange salmon (skin side up if it has skin) in a single layer onto a rimmed baking sheet and broil until lightly browned and flesh is opaque throughout, 8–10 minutes.
To serve, scoop cooked rice into bowls. Divide salmon, drained pickled cucumbers, and 2 thinly sliced avocados among bowls; spoon some cucumber pickling liquid over.
Drizzle with reserved spicy yogurt and top with sliced green onions and toasted sesame seeds.