Dredge the chicken pieces lightly with flour. Heat the oil in a frying pan and saute the chicken until golden. Transfer to a heavy casserole.
Saute the onion and garlic in the frying pan and add the chicken. Pour off and disregard an oil remaining in the pan and deglaze it with the rum, scraping to get up all the brown bits. Pour this into the casserole.
Add the cucumber pickles, hot peppers, cinnamon stick, anise, salt and pepper to taste, the pineapple juice, and chicken stock. Cover, and simmer gently for half an hour or until the chicken is almost done.
Add the pineapple pieces, bananas, and grapes and continue to cook, partially covered, for 15 minutes longer.
Remove the cinnamon stick. Arrange the chicken on a warmed platter with the fruit and some of the sauce. Garnish the platter with a ring of avocado slices and serve the remaining sauce seperately. Accompany the dish with plain white rice. Serves 6.