Federal Aviation Administrator J. Lynn Helms and other FAA officials have caused an uproar in the airline industry because of the way they handed out more than one-quarter of Braniff International's valuable airport landing rights in the past week.

Yesterday, federal transportation officials were drawing up new rules to distribute the Braniff landing rights, or slots.

Although an FAA spokesman said the slots had been distributed on an "emergency basis" following Braniff's financial collapse last Wednesday, industry sources complained yesterday about the closed-door nature of the agency's actions.

They also protested that Helms and the FAA, by giving specific Braniff routes to airlines that promised to serve them, seemed to be violating the tenets of the Airline Deregulation Act. The law is designed to leave the selection of routes to the airlines, based on marketplace needs.

The FAA reportedly distributed between 25 and 30 percent of Braniff's slots. Although the airlines almost immediately began flying and advertising their new routes, the FAA has refused to say how many of Braniff's 411 slots--160 of them are at Dallas/Fort Worth--were distributed, which airports were involved, or which airlines got them. The FAA said the information is "proprietary."

J.E. Murdock III, the FAA's chief counsel, denied that there was any impropriety in the FAA slot awards. "We got applications and gave them out," he said, noting that the awards were made for a renewable seven-day period to fill gaps left by Braniff's shutdown, with the understanding that the slots could be taken back in 24 hours.

Critics contended that most of Braniff's routes already were served by multiple airlines and that few specific gaps needed to be filled. According to the Civil Aeronautics Board, Braniff operated only two monopoly routes--Dallas to Omaha and to Wichita--which Texas International Airlines started flying this week.

One industry source said that even some airlines that received Braniff slots were unhappy about the process, but reluctant to speak up and get their slots taken away.

One airline source said that United Airlines already was flying two new routes--Denver and Chicago to Dallas--Friday morning, before most carriers had received word from the FAA that it would accept applications.

Delta Airlines is said to have sent the FAA a telegram Tuesday complaining about the process used to dole out Braniff's slots. William D. Berry Jr., Delta's manager for public relations, confirmed that the Atlanta-based airlines did "send a message to the FAA stating Delta's opinions" about the way in which the slots were allocated, but he declined to disclose the contents. Delta was given enough slots to operate one round trip from Dallas to Kansas City, one to Orlando and two to Memphis, he said.

Finding that their commuter airline members got no slots from the FAA, the Regional Airline Association filed objections with the FAA, along with a Freedom of Information Act request to find out how slots were distributed and what airlines got what routes. However, a spokesman said the request was withdrawn after the group was assured that a procedure was being drawn up for the longer-term allocation of slots that "will give everyone a chance to apply."

The new plan being devised reportedly will give out Braniff's slots for a 30-day period, subject to renewal and 24-hour cancellation.