Southern Railway yesterday reported record profits in 1980, partly because of a sharp increase in coal tonnage. Directors of the Washington-based company, which is planning a merger with Norfolk & Western, also increased Southern's dividend rate by 15 percent.

Avemco Corp., an aviation insurance holding company in Bethesda, posted record fourth-quarter profits but lower earnings for all of 1980, while Flow General of McLean said profits were higher for both the quarter and six months ended Dec. 31.

Fourth-quarter earnings of Southern were a record $44.1 million ($2.82 a share) compared with $33.3 million ($2.13) a year earlier as revenues rose 8 percent to $430 million. For the full year, the rail transportation firm listed profits of $181 million ($11.57 a share), up 12.6 percent from $161 million ($10.39). Revenues increased 11.6 percent to $1.64 billion.

The quarterly dividend rate was boosted 14 cents a share to $1.06, starting with a distribution on March 15 to stockholders of record Feb. 13.

Coal revenues rose about $61 million during the year and accounted for 16 percent of all Southern freight traffic compared with less than 14 percent in the previous year. Other substantial gains were in food and farm products, but the gains were offset largely by declines in hauling new automobiles and parts and petroleum products.

Southern President Harold Hall said yesterday that while any projections for 1981 must be tempered by "the reality of continued sluggishness in important segments of the economy," he has "firm confidence" in the long-term future. He noted that Southern plans $310 million of capital spending this year on top of more than $1 billion of such spending in the prior four years.

Avemco Corp. posted earnings in the final three months of 1980 of $1.1 million (44 cents a share) compared with $883,000 (36 cents) a year ago, a gain of 25 percent. For the year, Avemco profits were $2.9 million ($1.16) vs. $3.3 million ($1.33).

Chairman Arnold Johnson noted that the fourth-quarter gain reversed the performance of Avemco in the third quarter, when the company earned 5 cents a share because of unusual weather conditions and an increase in aircraft usage for intercity travel which created more insurance claims throughout the summer.

"We are happy to report that our fourth quarter and January to date have shown a return to a more normal pattern of aviation losses," said Johnson, whose firm sells aviation insurance, finance services and product marketing. Premiums written last year were a record $31.5 million, up 25 percent.

Flow General reported profits in the second fiscal quarter ended Dec. 31 of $1.9 million (25 cents a share) compared with $825,000 (15 cents, on fewer shares outstanding) as sales rose to $25.6 million from $17.9 million. Six-month earnings of the Northern Virginia scientific research and manufacturing firm rose to $3.3 million (47 cents) from $1.5 million (29 cents) as sales rose to $48.3 million from $34.6 million.

Noxell Corp. of Baltimore reported a 10 percent increase in profits during 1980. Earnings of the cosmetics manufacturer were $14.7 million ($3.01 a share) compared with $13.3 million ($2.67) in 1979 as sales rose to $204 million from $180 million. Fourth-quarter earnings were $2.8 million (58 cents) vs. $2.1 million (43 cents) as sales advanced to $45 million from $39 million.

Baltimore Gas and Electric Co. reported earnings of $117.3 million ($3.64 a share) for the year ended Dec. 31 compared with earnings of $106.5 million ($3.40) in 1979.

Total unit gas sales increased 1.8 percent, and total operating revenue grew from $1 million to $1.2 million.

United Bank and Trust Co. of Oxon Hill said 1980 profits rose to $581,498 ($5.58 a share) from $511,573 ($4.91), a gain of about 14 percent. Assets rose 13 percent to $45.5 million. Directors declared an extra cash dividend of 50 cents a share, payable Feb. 28, and a 5 percent stock dividend, payable May 1 if approved by stockholders in March.