Remove neck and giblets from chickens, hens, or quail if present; reserve for another use or discard. Pull off and discard any lumps of fat from birds. With poultry shears or kitchen scissors, cut along one side of backbone on each bird, cutting back completely in two; for chickens, cut along other side of backbones as well and discard backbones. Rinse birds well and pat dry. Pull birds open and set skin side up on a flat surface; with your hand, press birds to flatten.
In a 9- by 13-inch baking dish, mix lemon juice, parsley, olive oil, garlic, basil, oregano, pepper, chili flakes, and 1/2 teaspoon salt. Rub mixture all over birds.
Place in dish, overlapping and stacking as needed. Cover and chill at least 30 minutes or up to 1 day.
Set birds, skin side down and side by side, on a 12- by 17-inch section of an oiled barbecue grill over a solid bed of medium coals or medium heat on a gas grill (you can hold your hand at grill level only 4 to 5 seconds). Set a 12- by 17-inch roasting pan, right side up, on birds. Distribute 4 clean bricks (5 to 6 lb. each) evenly in pan (see notes).
Cover grill and cook until skin is well browned (lift pan to check), about 20 minutes for chickens, 18 minutes for hens, and 12 to 15 minutes for quail.
Remove weighted pan and, with a wide spatula, turn birds over. Cover grill and cook without weighted pan until meat at thigh bones is no longer pink (cut to test), 5 to 10 minutes longer for chickens and hens, 2 to 5 minutes for quail.
Transfer birds, skin up, to a platter. With a knife or poultry shears, cut chickens into quarters and hens into halves if desired.
