Season the chicken with the salt and black pepper and dust it lightly with the flour, shaking off excess.
Heat the olive oil in a large skillet and brown the chicken in batches, about 2 minutes per side.
Transfer the chicken to a 6-quart slow cooker and add the broth, garlic and capers.
Cover and cook on low until the thickest piece reaches 165°F, 2 1/2 to 3 hours.
Move the chicken to a warm platter and switch the cooker to high with the lid off for 8 minutes.
Stir in the lemon zest and juice, turn off the heat and swirl in the cold butter a few pieces at a time.
Spoon the caper sauce over the chicken and serve immediately.