Combine all vegetables in the bottom of a 5-quart slow cooker.
Whisk together 2/3 of the leek soup mix with the condensed soup and wine. Pour over vegetables. Cover and cook on LOW setting for 4 hours.
Heat oil in a large skillet. Combine the rest of the leek soup mix with some flour. Dredge chicken fillets in flour mixture and place in skillet. Cook for about 2 1/2 minutes each side.
Remove vegetables from slow cooker and arrange in a serving dish. Top with chicken.