If black America were a country, it would rank 16th in the world in the number of people living with the AIDS virus, the Black AIDS Institute, an advocacy group, reported yesterday. The report, financed in part by the Ford Foundation and the Elton John AIDS Foundation, provides a startling new perspective on an epidemic that was first recognized in 1981. Nearly 600,000 blacks are living with HIV, the virus that causes AIDS, and up to 30,000 are becoming infected each year. When adjusted for age, their death rate is 2 1/2 times that of infected whites, the report said. Partly as a result, the hypothetical nation of black America would rank below 104 other countries in life expectancy.