Cut figs into quarters and place in a small bowl; cover with hot water and soak until soft, about 15 minutes. Lift figs from liquid and place in a blender or food processor. Add 1/3 cup of the soaking liquid (discard remainder) and the broth, coriander, and dry mustard; whirl until smooth.
Rinse chicken and pat dry. Set a 10- to 12-inch nonstick frying pan over high heat. When hot, add 1 1/2 teaspoons olive oil and tilt pan to coat bottom. Add chicken in a single layer and cook, turning once, until browned on both sides, 4 to 6 minutes total. Transfer to a plate.
Reduce heat to medium-high. Add remaining 1 1/2 teaspoons oil and onion; stir often until onion is limp and beginning to brown, 2 to 3 minutes. Add flour and stir to coat onion. Add fig mixture and stir until boiling.
Return chicken to pan. Cover and simmer over low heat until chicken is no longer pink in center of thickest part (cut to test), 5 to 7 minutes.
With tongs, transfer chicken to plates. Stir sherry into sauce. If desired for a smoother sauce, pour through a fine strainer into a bowl. Spoon sauce equally over chicken, then drizzle each portion with 1 tablespoon vinegar. Sprinkle with chives and add salt and pepper to taste.