Thaw shrimp and scallops, if frozen. Peel and devein shrimp, leaving tails intact if desired. Halve scallops horizontally. Rinse shrimp and scallops; pat dry with paper towels. Set aside.
In a large resealable plastic bag combine the flour, paprika, 1/4 teaspoon of the salt, the sugar, black pepper, and cayenne pepper. Seal bag; shake to combine. Add shrimp and scallops to the bag Seal bag; shake to coat shrimp and scallops. Set aside.
Melt 1 tablespoons of butter in a large nonstick skillet over medium-high heat. Add garlic and the remaining 1/4 teaspoon salt; cook and stir for 30 seconds. Add shrimp and scallops to the pan in an even layer; cook for 2 minutes. Stir in tomatoes, broth, vermouth, and lemon juice; cook for 2 to 3 minutes or until shrimp and scallops are opaque, stirring occasionally. Remove from heat; stir in the remaining 1 tablespoon butter, the parsley, and chives.
Serve in shallow bowls with hot cooked brown rice.