To make fresh herb sauce: In small bowl, combine dill, parsley, chives, garlic, salt, red pepper flakes, lemon zest, lemon juice and olive oil; set aside.
Set both sides of grill to 650 F (high) and close lid.
To prepare branzini: Season fish inside and out with kosher salt. Fill cavity of each fish with lemon slices, dill sprigs and parsley sprigs then tie with kitchen twine to secure. Refrigerate until ready to grill.
Evenly coat skin of both fish with olive oil. Insert temperature probe into thickest part of flesh of each fish, parallel to dorsal fin, then place on grill with belly sides toward you. Close lid and cook 5 minutes.
Open lid and gently turn fish over with thin metal spatula or two forks. Close lid and cook 5 minutes, or until internal temperature reaches 145 F.
Transfer fish to platter and remove twine. Serve fish topped with fresh herb sauce.