Kevin Brennan was born at Beechworth, and educated at Xavier College and the University of Melbourne. After graduating in 1923, he joined the staff of the Queen's Memorial Infectious Diseases Hospital, Fairfield, where he served as resident medical officer from 1924 to 1925. From 1925 to 1929, he was employed as a medical officer in the Education Department. After qualifying for the Diploma of Public Health, he became medical officer of health and tuberculosis officer for the city of Bendigo from 1929 to 1930. He was appointed to the Department of Health in 1934, as district health officer and served in the northern health areas until 1942. He married Grace, the daughter of J Graham, in 1937, and set up his home in Ballarat.

In 1942, on the request of the Department of the Army, he joined the staff of the Medical Directorate at Army Headquarters for duty with the Director of Hygiene. He served both in Australia and in New Guinea and was released in 1945, with the rank of major to rejoin the Department.

Whilst on active service he contracted rheumatoid arthritis and this flared extensively so that he retired from the public service in 1946. However despite severe pain, he resumed duties part-time early in 1948. At this time, he also held a part-time appointment as lecturer at the Sydney School of Public Health and Tropical Medicine.

In 1950, Brennan, now senior health officer of the general health branch, was awarded a travelling fellowship by the National Health and Medical Research Council to study public health work and administration overseas. Subsequently his work in public health took him around the world another two times.

In 1952, he was appointed as chief health officer and chairman of the Commission of Public Health, in which positions he continued to serve until his retirement in August 1966. From 1952 to 1964, he served on the Victorian branch council of the Australian Medical Association and was elected as a Fellow of the Australian Medical Association in 1969. Dr Brennan remembered the poliomyelitis epidemic of 1937, as horrible and frightening, for during this epidemic the death rate and paralysis rate were the highest ever recorded. Later he used his influence to ensure that Australia was one of the first countries to receive Salk vaccine and to undertake clinical trials of the vaccine. As a person Kevin was a 'bon vivant', and a charming and amusing host. He was a keen racegoer, a Melbourne football supporter and a member of several golf clubs.