In a large bowl, stir rice in cool water; drain. Repeat several times until water is no longer cloudy. Drain rice.
In a 2- to 3-quart pan, combine rice and 3 cups water. Bring to a boil over high heat, cover, and turn heat to lowest setting. Cook until rice is tender to bite, about 15 minutes; do not stir.
Pour hot rice into a colander to drain; let stand until warm, about 15 minutes, or cool.
In a wide bowl, combine orange and lime juices, sugar, and 1/4 teaspoon nutmeg. Cut peel from mangoes, then cut fruit in small pieces into bowl; discard the pits.
Pour rice into bowl, mix, and add salt to taste. Sprinkle salad with more nutmeg, then flowers.