Carb Cleaner or brake cleaner down the tube followed by compressed air.
I have done that and I suspect improved nothing.
Back in the 60's when the M16 was first fielded, Remington/Dupont (page 147 of the Black Rifle) provided IMR 4475 for the cartridges. The M16 even though it had been fielded was still an underdeveloped rifle system and required powder tolerances that exceeded state of the art process controls. Remington/Dupont could not hold the tolerances for each and every lot and instead hand selected lots from production to load for the .223 round.
When Remington no bid, for reasons in the Black Rifle Book, the Army was left with WC846 to use. This powder worked fine in M14's but the pressure curve was out of tolerance for the M16 and it left a lot of residue in the gas tube.
That took time, and a number of dead GI's to figure out, but eventually the powder was cleaned up and today's powders are a lot cleaner. It is hardly worth the effort to clean the gas tube.
Unless you are obsessive, such as I, about your rifle maintenance.