Preheat the oven to 450°F (230°C).
Place the halved potatoes in a large saucepan and cover with cold water. Add a pinch of salt, bring to a boil over medium-high heat, and cook until just tender, about 8 minutes. Drain and set aside.
On a cutting board, strip about 1 tablespoon of rosemary leaves from the sprigs and pile them with the smashed garlic, 2 teaspoons sea salt, and the red pepper flakes. Mince and mash them together with a knife to form a coarse paste.
Transfer the paste to a bowl, stir in the juice of 1 lemon and the olive oil, then add the chicken breasts and turn to coat evenly with the mixture.
Heat a large cast-iron or ovenproof skillet over medium-high heat. Add the chicken and cook, covered, until browned on the first side, about 5 minutes.
Turn the chicken. Add the par-cooked potatoes to the skillet and drizzle with the juice of the remaining lemon. Tuck the remaining rosemary sprigs and the squeezed lemon halves into the skillet around the chicken.
Transfer the skillet to the preheated oven and roast uncovered until the chicken is cooked through and reaches an internal temperature of 165°F (74°C), about 25 minutes.
Remove from the oven and let rest briefly before serving.