Rinse the rice until the water runs mostly clear, soak for at least 30 minutes, then drain.
Sprinkle the salt over both sides of the fish and refrigerate for 15 minutes. Pat dry with a paper towel.
Heat the oil in a frying pan over medium heat. Sear the fish skin-side down until golden, then flip and cook the other side for about 1 minute. It does not need to be cooked through.
Put the rice in the rice cooker pot. Add the soy sauce, sake, mirin and a pinch of salt first, lay the kombu on top, then add water up to the 2-cup line. Stir once.
Set the seared fish on top, skin-side up, and cook on the normal white rice or mixed-rice setting. Do not stir once the fish is in.
When the rice is done, lift out the fish and kombu. Remove the skin and all bones, flake the flesh, return it to the pot and fold it through the rice gently. Serve topped with green onion.