Preheat oven to 375°F.
Season chicken with salt and pepper; lightly dust with flour, shaking off excess.
Heat oil in a braiser pan or a large straight-sided ovenproof skillet over medium-high.
When it shimmers, add chicken, skin-side down, in a single layer.
Cook, flipping once, until browned on both sides, 6 to 8 minutes total. Transfer to a plate.
Add sausages to pan and cook, turning a few times, until browned all over but not cooked through, about 5 minutes; transfer to plate with chicken.
Reduce heat to medium; add shallots and garlic to pan and cook, stirring occasionally, until soft and golden in places, about 3 minutes.
Add rosemary and pepper brine; cook until liquid has mostly evaporated, a few seconds.
Add broth and lemon juice; boil until reduced by half, 8 to 10 minutes.
Return chicken and any accumulated juices to pan, skin-side up, along with peppers.
Transfer pan to oven; roast 15 minutes.
Meanwhile, slice sausages on the bias into thirds; nestle into skillet.
Continue cooking until a thermometer inserted in chicken (near but not touching bones) registers 165°F and sausages are just cooked through, about 5 minutes more.
Serve warm with bread.
