In a pan, combine beef stock and chicken stock. Bring to boil and let simmer until mixture is reduced down to 1/2 cup. Set stock reduction to the side.
While stock is reducing on the stove,lightly score fat side of duck breast, with a sharp knife, in a diamond pattern. Sprinkle duck breasts with thyme, garlic, paprika, salt and pepper to season. Let sit, for 20minutes.
In a hot skillet pan, heat to medium high. Add olive oil. Add duck breast, fat (skin) side down, and cook for 6 minutes.
Turn duck over and let cook 2 minutes.
Remove duck breast to foil lined baking pan, meat side down, and bake in oven for 5-6 minutes. Remove from oven and let rest on cutting board for at least 5minutes.
Meanwhile in skillet, drain off most of fat. Add 2tbsp of butter to pan.
Add shallot and cook until tender.
Add port wine and bring to a boil. Reduce by half.
Add 1/2 cup stock reduction and bring mixture to a boil. Simmer sauce low until reduced by 1/3 or sauce is a syrupy glaze.
Add fig preserves. Stir until completely melted and combined into sauce.
In a cup combine remaining 1 tbsp flour and 1 tbsp butter (beurre manie).
Add flour mixture to sauce and stir well to combine. Bring sauce to boil, stirring, until sauce thickens. That will take only 2 minutes or so. Remove from heat.
Cut duck breast, into 1/2 inch slices, angled, against the grain.
On serving plates, place sauce on bottom and place several slices of duck breast on top. Drizzle just a bit more sauce over top of duck slices. Repeat on all serving plates.