In a large stock pot over high heat, boil water for pasta. When boiling, salt the water heavily and add the pasta.
Meanwhile, in a medium size bowl, mix kosher salt, black pepper, red pepper flakes, paprika and 1 teaspoon dill with 1/2 cup flour. In another medium bowl, add water. Wet chicken with water and then dredge in the flour mixture.
In large saute pan over medium-high heat, melt 4 tablespoons of butter and saute chicken breasts, about 4 minutes on each side. After they are cooked, remove to a plate. Add to the same pan the shallots and remaining dill. Stir in remaining flour and mix until pasty. Add dry vermouth. After alcohol burns off, mix in mushrooms. Add chicken stock and lemon juice and cook for an additional 3 to 4 minutes. Turn off the heat and stir in the remaining 2 tablespoons butter and a pinch of parsley. Season with salt and pepper, to taste.
Remove pasta from water after cooking for approximately 10 to 12 minutes. Toss in oil to coat the pasta and add lemon zest. Put pasta on serving platter, then lay chicken across top and pour the sauce over the top. Garnish with parsley.