Preheat the grill to medium and brush clean with a wire brush.

In a saucepan, combine the rum, sugar, orange and lime juices, and simmer, stirring, to dissolve the sugar. Cook for 3 to 4 minutes to slightly thicken. Let cool.

Place pineapple on the grill. Cook until lightly charred and golden, basting on both sides with the rum mixture, 6 to 8 minutes.

Remove from the heat and arrange the pineapple slices in shallow bowls. Top the pineapple slices with a scoop of ice cream, drizzle a spoonful of the remaining rum glaze on top, and garnish with toasted coconut flakes. Serve immediately.