Rinse meat and rub salt evenly onto all sides. Cover and chill for 2 to 3 hours. Rinse meat well and pat dry. Rub all over with oil.
To cook brisket, turn a gas grill to high, close lid, and heat for 10 minutes. Turn off all but one perimeter burner and reduce heat to medium or low to maintain a temperature of 225º to 250º (check with a grill thermometer or external barbecue thermometer, and open lid as needed to let temperature drop during cooking). Lay brisket, fat side down, on grill as far from flame as possible. Close lid and cook, turning brisket about every 1 1/2 hours, until meat pierces easily with a sharp knife (it will be firm but not hard) and is lightly browned, 5 to 5 1/2 hours total.
To cook flank steak, lay meat on a barbecue grill over a solid bed of hot coals or direct high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds); close lid if using a gas grill. Cook, turning once, until flank steaks are done to your liking (cut to test), 7 to 9 minutes total for medium-rare.
Transfer meat to a platter and let stand at least 5 minutes. Cut into thin slices.
Nutritional Analysis per serving of flank steak.