Bring rice and water to a boil in a medium saucepan. Cover, reduce heat, and simmer 15 minutes. Remove from heat; let stand, covered, 15 minutes.
Place rice in a large bowl, and gently stir in rice vinegar with a spoon until combined. Cover rice mixture, and let rest 30 minutes.
Sprinkle crabs with salt and black pepper. Dredge crabs in flour, shaking off excess flour.
Melt butter in a large nonstick skillet over medium-high heat. Add crabs, top sides down; cook 3 minutes, gently pressing body and legs against pan. Turn crabs over; cook 3 minutes. Cut each crab into quarters, leaving legs attached.
Cut off top quarter of nori sheet along a short end. Place nori, shiny side down, on a sushi mat covered with plastic wrap, with a short end toward you. Pat 3/4 cup rice over nori with moist hands, leaving a 1-inch border on short end of nori closest to you.
Arrange 4 crab pieces and 4 avocado slices horizontally over rice, allowing crab legs to extend over long edges of nori. Sprinkle each sheet with 2 tablespoons green onions and 1 teaspoon sesame seeds.
Lift short edge of nori closest to you; fold over filling. Lift bottom edge of sushi mat; roll toward top edge, pressing firmly. Continue rolling to top edge; press mat to seal sushi roll. Slice each roll into 8 pieces with a sharp knife.