Avemco Corp., a national aviation insurance and financial services firm based in Bethesda, reported record fourth-quarter and 1981 profits yesterday.

In a separate report, Flow General Inc., a diversified scientific research and manufacturing firm based in McLean, also reported increased profits for the six months and quarter ended Dec. 31.

Avemco's net earnings in 1981 were $3.8 million ($1.53 a share), up 32 percent from $2.9 million ($1.16) in 1980. Revenues were a record $30.7 million in 1981, 17 percent more than $24.2 million in 1980.

Net earnings in the October-December 1981 period were $1.2 million (49 cents), the highest for any quarter in Avemco's history, the company said. The results compared with earnings of $1.1 million (44 cents) for the corresponding period of 1980. The fourth-quarter period is traditionally Avemco's best.

Arnold H. Johnson, Avemco's chairman, attributed the strong showings to substantial investment income growth and continuation of favorable underwriting profits in the insurance subsidiary, which wrote a record $40.4 million in gross insurance premiums in 1981, up 28 percent from $31.5 million--the previous record--in 1980.

Johnson said that, despite the recession, Avemco generated increased premium volume not only on the single-engine and light twin-engine aircraft it has insured traditionally, but also on larger corporate turbo prop and jet aircraft.

In its report, Flow General reported profits of $2.3 million (28 cents a share) in the second fiscal quarter ended Dec. 31, up 24 percent from $1.9 million (25 cents) in the corresponding quarter of 1980. There were 8.5 million average shares in the 1981 period compared with 7.5 million in the 1980 period. Sales rose 19 percent during the quarter to $30.6 million.

Flow General manufactures and sells biomedical equipment and biological products, specialized equipment for the broadcast industry and materials-testing equipment. The firm's biomedical subsidiary, Flow Laboratories, has been involved in producing interferon, considered a potential cancer-fighting agent, for the government.

The company said net income for the six months ended Dec. 31 totaled $4.7 million (56 cents), up 45 percent from $3.3 million (47 cents) in the corresponding 1980 period. Per-share earnings were based on 8.4 million average common shares in the 1981 period and almost 7 million shares in the 1980 period. Sales totaled $60.9 million in the 1981 July-December period, up 26 percent from the same 1980 period.