A civil engineer walked for six days through the bush - avoiding main roads, sleeping under trees and eating roots - to escape from Uganda and what he is sure would have been a burtal death at the hands of secret police.

A senior police officer fled by dressing as a woman and bluffing the secret police of Uganda's President Idi Amin Dada, who set up roadblocks every 10 miles on the highway between the capital city of Kampala and the Kenyan border. Through a window, he saw the police chop off the head of a man who was hiding him.

By teh thousands, refugees such as these two men are streaming into Kenya to avoid the brutal regime of Amin. THey feel they face death or torture at home. Here they face a hard life in a country that already has more refugees than it can handle.

There is no good estimate as to the number of people who hav fled Uganda since Jan. 26 - the sixth anniversary of the military coup that put Amin in power and the date his latest reign of terror started.

Official Kenyan and U.N. officials here list the number of refugees since January at about 600, but acknowledge that many people do not bother to register. Ugandan sources here, who try to keep track, estimate that there are close to 10,000 refugees in this country. The actual number probably is somewhere in between.

These refugees from tribal and religious genocide in Uganda join millions of other Africans who have been forced to flee their countries during the past 20 years.

There already are 2 million African refugees, most of them blacks fleeing from black governments because of religious, tribal or political persecution. According to statistics compiled by church and other humanitarian groups here, one of every 130 African adults has fled his country, giving this continent the worst refugee problem in the world.

Among the most prominent refugees is former Ugandan President Milton Obote, the man Amin threw out of office in 1971. He now lives in Tanzania, where he has been accused of trying to launch at least one coup to topple Amin.

Tanzania, which can barely feed its own citizens, has one of the best records in Africa for accepting and caring for refugees.

It took in 120,000 Hutos, who were forced to flee Burundi, in central Africa, five years ago when the ruling tribe there tried to eliminate them. They are housed in two crowded refugee camps. In all, Tanzania has almost 200,000 refugees within its borders.

Presently thousands are fleeing from Ethiopia. Sudan alone is caring for 100,000 Eritreans who fled Ethiopia in the past two years, after Eritrean nationalist groups tried to secede from the country. Now, however, many are fleeing a political bloodbath in Ethiopia.

"I am a refugee," says Sisey Abebe, 24, a student who fled Ethiopia in September after his father and one brother were killed and two other brothers jailed. They were accused of belonging to the opposition Ethiopina People's Revolutionary Party.

Abebe now lives on $12.50 a month in aid he receives from the U.N. High Commission on Refugees, which spends half its 16 million annual budget for world refugees in Africa. With that $12.50 Abebe rents an eight-foot-square room with six other Ethiopian refugees.

He often is given meals by refugee friends who get money sent in. Otherwise, eh said, he lives on potato chips although he appears reasonably healthy. Abebe said he looked better when he arrived here: "I had some meat on my bones then."

Most Ugandans face the same sort of life here, where there are not enough jobs for all the Kenyans who want to work. Many Ugandans, however, do not come to Nairobi, but settle instead in trading centers near the border where it is less expensive to live and they are more likely to find some sort of day labor.

But they do not settle too close to the frontier, said Deputy District Commissioner Frederick C. K. Waiganjo in the border town of Busia, because they fear that Amin's dread secret police, named the State Research Bureau, will sneak into Kenya and kidnap them.

Most refugees here do not like to admit they are Ugandans because they think they may be harassed by Amin's police. There was a report this week in the Daily Standard newspaper that members of the State Research Bureau had posed as refugees to get here.

It is not hard to cross the border between Uganda and Kenya. Except for the crossing points on the highways, the border is unmarked. It is all bush, and Ugandan territory looks the same as Kenyan.

Among the most prominent refugees fleeing Uganda have been five of the 18 Anglican bishops who publically criticized Amin last month. Amin, a Moslem, has been ruthless in dealing with Christians as well as with members of the Acholi and Lango tribes.

A high police official from Uganda who settled here told the Daily Nation last week that Amin's "master plan" is to eliminate all 1.5 million Acholi and Lango males over nine years of age and all Anglicans who hold high posts in the government, the army or in the private sector such as the church.

Most of the news of Uganda comes via these refugees, and every sensational detail is printed by the two daily papers here. While many indepent observers believe Amin is capable of almost any atrocity, they are skeptical that many of the charges printed in the local press may be exaggerated by the refugees to justify their fleeing the country and leaving their wives and children behind!

But there is no question that fear is causing people to flee Uganda. An estimated 2,000 to 5,000 persons have been killed there since January, sources here believe, and the prisons are filled with Acholis and Langis picked up for no other reason than the tribes they belong to. These tribes provided the main support for Obote, the former Ugandan president.

The exodus has robbed Uganda of many of its intellectual elite, its doctors, engineers and civil servants. They fled. Now, according to sources here, impoverished village farmers also are leaving the country.