The federal regulation says that the passengers can only drink alcohol that is served to them by a crewmember. This is so the crewmembers have the ability to cutoff a passenger who has had too much to drink before it becomes a problem.

BYOB can be accommodated by the passenger(s) giving their alcohol to the F/A and having the F/A serve it to them during the flight. I'm not aware of any US airlines that currently offer this service on scheduled flights.
.
.

14 CFR 121.575 Alcoholic beverages.

(a) No person may drink any alcoholic beverage aboard an aircraft unless the certificate holder operating the aircraft has served that beverage to him.

(b) No certificate holder may serve any alcoholic beverage to any person aboard any of its aircraft who—

(1) Appears to be intoxicated;

(2) Is escorting a person or being escorted in accordance with 49 CFR 1544.221; or

(3) Has a deadly or dangerous weapon accessible to him while aboard the aircraft in accordance with 49 CFR 1544.219, 1544.221, or 1544.223.

(c) No certificate holder may allow any person to board any of its aircraft if that person appears to be intoxicated.

(d) Each certificate holder shall, within five days after the incident, report to the Administrator the refusal of any person to comply with paragraph (a) of this section, or of any disturbance caused by a person who appears to be intoxicated aboard any of its aircraft.