For easy clean-up, place a cooking liner in your slow cooker.
Stir together flour, salt, and pepper. Dredge chicken in flour mixture, shaking off excess.
Heat butter and oil in large nonstick skillet over medium-high. Add chicken breasts; cook until golden brown, 5 to 6 minutes per side. Transfer chicken breasts to a large slow cooker.
Top chicken in slow cooker with broth, wine, capers, and lemon juice. Cover and cook on low for 4 hours or until chicken is cooked (internal temperature of 165°F).
Place chicken on a serving platter and keep warm. Transfer cooking liquid to a medium saucepan. Whisk together cold water and cornstarch in a small bowl until smooth. Add to slow cooker liquid and stir to combine. Bring to a boil over high; cook, stirring occasionally, until reduced to 3 cups, 6 to 10 minutes. Spoon sauce over chicken.