Heat oil in a large skillet over medium-high heat. Season chicken with salt and pepper, then coat with flour. Fry in hot oil until browned, turning as needed. Reduce heat to medium, cover, and cook until meat is tender and juices run clear, about 25 minutes.

Remove chicken from the skillet; pour off all but 1/4 cup drippings. Return the skillet to medium heat and stir in cherries, reserving some cherry liquid for later. Stir in sugar and bring to a boil. Dissolve cornstarch in reserved cherry liquid, then stir into the skillet. Cook, stirring gently, until thickened.

Add orange slices and almonds to the skillet, then return chicken pieces to the skillet. Spoon sauce over chicken to coat; simmer over low heat for 5 to 10 minutes before serving.