Preheat oven to 350°.
Remove stems from figs; discard stems. Coarsely chop figs. Combine figs, wine, and juice in a medium saucepan; bring to a boil over medium heat. Reduce heat, and simmer, uncovered, until figs are tender and most of liquid is absorbed (about 20 minutes). Remove from heat. Cool slightly. Place fig mixture in a food processor; process until smooth. Spoon into a bowl; cool completely.
Lightly spoon flour into a dry measuring cup; level with a knife. Place flour, oats, sugar, and cinnamon in a food processor; process until oats are finely ground. Add butter; process until mixture resembles coarse meal. Add egg white; pulse to combine. Firmly press half of crumb mixture into an 8-inch square pan coated with cooking spray. Spread fig mixture over crumb mixture. Sprinkle with remaining crumb mixture; press gently. Bake at 350° for 25 minutes. Cool completely on a wire rack.