Combine first 5 ingredients in a large bowl; let stand 1 hour.
Roll up each flounder fillet jelly-roll fashion, and place in a large skillet. Add green onions, carrot, and shallots to skillet. Strain tea mixture through a sieve into skillet; bring to a boil. Reduce heat to medium-low, and simmer, uncovered, 8 minutes or until fish flakes easily when tested with a fork. Remove fish, green onions, and carrots from skillet with a slotted spoon, and place on a serving platter. Serve with Thai Scallion Sauce.