In a large skillet over medium heat, melt butter . Stir in bananas and sugar, and stir until sugar is dissolved. Pour in rum and cook 1 to 2 minutes more. Spoon half the banana mixture onto each flour tortilla, and roll up, tucking in the ends, like a burrito.
In a large skillet, heat the vegetable oil over medium-high heat. Fry chimichangas until golden. Drain on paper towels. Serve warm.
