Place flour in a shallow dish and stir in 1 teaspoon lemon zest. Season pork with salt and pepper, then coat with flour, shaking off excess.
In a large skillet, heat oil and 1 tablespoon butter over medium-high. In batches, cook pork until browned and cooked through, about 2 minutes per side. Transfer to a plate and tent loosely with foil.
Reduce heat to medium, add garlic and remaining tablespoon butter, and cook until fragrant, 30 seconds.
Add broth and cook, stirring, until reduced by half, 4 minutes. Return pork to pan along with any accumulated juices and lemon slices; cook until sauce has thickened slightly, 2 minutes. Add 1 tablespoon lemon juice, season with salt and pepper, and sprinkle with chives.