Measure the flour into a pie plate. In a Pyrex measuring cup, combine 1/4 cup of the pineapple juice with the rum, sugar, and nuts; set aside.

Pat the pineapple dry. One at a time, lightly dredge the pineapple rings in the flour and put them on a wire rack. Heat the butter and oil over medium heat in a 12-inch skillet. When the butter begins to darken slightly, increase the heat to medium high and add the pineapple rings to the skillet. Saute until golden brown on one side, 2 to 3 minutes; turn the pineapple over and saute until golden brown on the other side, 2 to 3 minutes longer. Transfer the pineapple to four dessert plates. Carefully add the rum mixture to the empty skillet; simmer and reduce until syrupy, 1 to 2 minutes. Remove from the heat and stir in the cream. Spoon a portion of the sauce over each plate and serve immediately with the ice cream.