To prepare duck, combine first 4 ingredients in a large zip-top plastic bag. Add duck; seal and marinate in refrigerator 2 hours, turning bag occasionally. Remove duck from marinade; discard marinade. Sprinkle salt evenly over duck. Heat a large nonstick skillet over medium-high heat; coat pan with cooking spray. Add duck; cook 2 minutes on each side or until desired degree of doneness.
To prepare chutney, while duck marinates, combine kumquats and next 5 ingredients (through jalapeño) in a saucepan; bring to a boil. Cover, reduce heat, and simmer 40 minutes. Add cherries; cover and simmer 15 minutes. Remove from heat; stir in basil, parsley, and 2 tablespoons lime juice. Serve warm or at room temperature over duck.