Preheat oven to 400°F. Rinse flounder, pat dry and place flat on a broiling pan lined with foil. Season flounder with salt and pepper.
Melt butter in a small saucepan over medium-high heat. Stir in lemon and lime zests and remove from heat.
Set aside 1 Tbsp. lemon-lime butter. Thoroughly brush 1 side of each fillet with remaining butter, dabbing brush so it collects some zest as well as butter. Turn and brush other side of each fish fillet.
In a small bowl, mix together bread crumbs and thyme with a fork. Sprinkle equal amounts of crumb mixture over each fillet and drizzle with reserved lemon-lime butter. Bake until fish is lightly browned on top and flakes easily when pierced with a fork, 12 to 15 minutes. Garnish with lemon and lime slices and serve with sides of roasted new potatoes and steamed broccoli, if desired.