The "Fly American Act" for federal workers traveling abroad should be grounded, say U.S. diplomats posted around South America, who complain that they are captive passengers aboard an uncaring Braniff International.

Under the law passed in 1974, official U.S. travel must be on American-flag airliners wherever available, and for much of South Africa that means only Braniff.

In an offensive carried on by angry cables, U.S. ambassadors from Quito to Buenos Aires are telling the State Department that the act - designed to keep travel dollars stateside - is costing the government dearly in time wasted, mail delayed and tempers frayed by planes that arrive late, overbooked or not at all.

The diplomatic campaign against Braniff was launched three months ago by Ambassador Robert E. White in a cable from Asuncion, Paraguay, that is now known among fellow envoys as "the shot heard "round the continent."

"Service to and from Asucion via Braniff is deplorable," White told the department, with copies forwarded to other posts along Braniff's route. The other envoys have been weighing in ever since and copies of the cables recently were made available to The Washington Post.

White and his cohorts call for a suspension of the "Fly American" rules so U.S. officials can take Latin and other lines - in some cases brief connector flights to Pan American service on the east coast of South America - until Braniff changes its ways.

White, asked if he stood by the unclassified cable traffic, did so emphatically, calling Braniff's service "a disaster. We had to call attention to it and we did," he said.

Braniff, while aknowledging some troubles in South America as it expands its service rapidly in the United States and elsewhere abroad, denied most of the diplomats' charges. Among them:

"Braniff's rapid expansion and lack of equipment is matched by their unacceptable level of service and non-concern for passenger comfort. Mission personnel can attest to poor inflight service, dirty planes, filthy upholstery, "scheduled" delays and lost baggage" - Ambassador to Argentina Raul Castro.

From Lima, where Braniff collects passengers from connector flights for the trip north - "On many occasions embassy personnel have observed Braniff loading passengers and then letting them sit...for very long periods while waiting for a delayed flight to arrive. Normally, when one boards an aircraft one expects to depart - but that's not the case with Braniff in Lima" - Ambassador to Peru Harry W. Schlaudeman.

From Santiago, Ambassador to Chile George W. Landau confirmed a local press account in late June of a Braniff DC8 "erroneously" landing at a domestic terminal instead of the international airport nine miles away. "There was some cause for concern since there were two small planes taking off and landing at the time the DC8 made its unexpected appearance," said Landau.

Ambassador to Ecuador Raymond E. Gonzalez, citing "Braniff's arrogance," described its attempt "to bump Elliot Richardson from a Quito-Miami flight for which he had confirmed and reconfirmed reservations." Deputy Undersecretary of Labor Howard Samule encountered "a series of typical misadventures (poor counter service and missed connections)...prompting him to write a letter of protest to Braniff's president," said Gonzalez.

The barrage of cables evoked a reply from Undersecretary of State Warren Christopher. He described promises made in discussions with Braniff's vice president for Latin America, Charles S. South, of new equipment and services.

White replied last month: "We take small comfort from the fact that the department is "encouraged by the concrete steps which Braniff is taking to upgrade its Latin American service." We can see no evidence of any intention" to improve, he said, adding, "The latest examples are the gross overbooking of flights. We have been told by Braniff representative that an overbooking of 100 seats on one flight led to a riot in Buenos Aires."

In New York, Braniff spokesman Louis Garcia called the complaints "undue and unjustified." He acknowledged that Braniff's fleet of DC8s is inadequate to new passenger demands and said 747 jumbo jets will soon replace them. The first 747 runs began last week.

Commenting on the charges of delayed mail, Garcia said the letters in question were low-priority personal correspondence that Braniff carries on a space-available basis.

A round-robin of White's cables had established that when a waiver was granted allowing LAN Chile airline to move out mail backlogged in a Braniff warehouse in Panama, embassy personnel started receiving letters mailed two months earlier.

White, in a phone interview, said he did not oppose the purpose of flying American "but we have to have a means of checking on them."

In a cable, though, White raised a point reinforced by officials in Washington that the State Department is more dogmatic than other agencies in complying with "Fly American," known formally and euphemistically as the International Air Transportation Fir Competitive Practices Act.

White declared: "Many U.S. travelers from other agencies seem never to have heard of the Act and anyone who has handled congressional delegations knows that the solons who wrote the law flout it continually."

A branch of the State Department is assigned to booking congressmen with tickets bought from American companies. However, an official acknowledged, "what airline they choose to fly once they're abroad is up to them."