The diplomatic flap surpassed anything a windless morning could provide when the flags of the nine invited participants in the Cairo conference were unfurled in front of the historic Mena House Oberoi Hotel here today.

Inside the hotel, only representatives of Egypt, Israel, the United States and the United Nations were present to mark the opening of the conference. In addition, the Egyptians chose to raise the flags of those who had been invited but refused to come.

Therefore, as the conference opened the flags of the Soviet Union, Jordan, Syria, Lebanon and the Palestine Liberation Organization hung limply on their poles beside those of the actual participants.

Rather than complain to the Egyptian government, the Israeli delegation, on official Foreign Ministry stationery, formally complained to the manager of the hotel that "an unidentified flag was flown not one representing any state."

The objection, of course, was to the flag of the PLO, which the Israelis refuse to recognize in any form or manner. The incident, the Israeli letter said, "could have spoiled the atmosphere prevailing at the conference, at which your government is host, and we trust that such an incident will not recur."

In true oriental fashion the problem was resolved by taking down all the flags. Had the Syrians attended the conference they also might have complained. For as television crews poked at the flags with sticks to photograph them better, it was suddenly noticed that instead of the Syrian flag the flag of North Yemen had been hoisted by mistake.

"The Syrians are sure to take this personally," an Egyptian correspondent moaned. An Israeli photographer speculated that the North Yemenis might actually arrive.

As for the managers of the 106-year-old hotel, where Roosevelt and Churchill met during World War II, their thoughts went unrecorded. Since the entire top management is Indian rather than Egyptian - the hotel is operated by the Indian Oberoi chain - the quarrel was not really theirs anyway. They had prepared 10th pole for their own Mena House flag, but someone had prevented it being hoisted alongside the Hage of the participants and they angry absentees.