Cook the rices in boiling salted water until done, about 15 minutes. Drain and place in a bowl.
Score the skin of the duck breasts with a knife and cook in a hot frypan, 4 minutes for the skin side and 2 for the other side. Place on a cutting board and cover with aluminium foil. Discard the drippings, then heat 1 teaspoon oil and saute the button mushrooms 3-5 minutes, stirring constantly. Transfer to the bowl with the rice and repeat with the shiitake mushrooms.
Zest one of the oranges to get 1 teaspoon zest. Peel the oranges and separate into segments. To the rice add the orange segments, water chestnuts and 1/2 the pomegranate seeds.
Make the dressing by combining the ginger, mustard, honey, oil, vinegar and zest in a small bowl. Add salt and pepper to taste. Toss the rice with 1/3 of the dressing.
Remove the duck skin and thinly slice the meat. Arrange over the rice, sprinkle with the remaining pomegranate seeds and drizzle with remaining dressing.