Kenney was born in West Palm Beach, Florida, the son of Estelle "Stephanie" (Karch) and Daniel "Harry" Kenney. He was named after General Douglas MacArthur. Kenney was of Irish and Eastern European descent. His family moved to Mentor, Ohio in the early 1950s, before settling in Chagrin Falls, Ohio, a suburb of Cleveland. Kenney lived in Chagrin Falls from 1958-1964 and attended Gilmour Academy, a Catholic prep high school for boys in nearby Gates Mills, Ohio.

To escape the pressures of running a successful magazine, Kenney sometimes took unannounced extended breaks, although, despite these absences, "Mrs Agnew's Diary" was always submitted to the Lampoon. During one of these breaks he wrote a comic novel, "Teenage Commies from Outer Space". Kenney threw the manuscript in a bin after a negative review from Beard. Beard later said that it was simply the wrong form and the spirit of the novel was channelled into National Lampoon's 1964 High School Yearbook, which Kenney co-wrote with P. J. O'Rourke.

While at Harvard University, Kenney was a member of the Signet society, President of the Spee Club, and Editor of The Harvard Lampoon. There, he was part of the first group of newcomers who restyled the college humor magazine. Another of these Writers was Henry Beard, with whom Kenney frequently collaborated, and who became a lifelong friend. Together with Beard, he wrote the short novel Bored of the Rings, which was published during 1969. Kenney graduated in 1968. Soon after, he, Beard and fellow Harvard alumnus Robert Hoffman began work on founding the humor magazine National Lampoon.

Kenney was one of the originating forces of what was to become known during the 1970s as the "new wave" of comedy: a dark, irreverent style of humor Kenney used as the basis for the magazine. Kenney was Editor-in-Chief from 1970 to 1972, Senior Editor 1973 to 1974, and Editor from 1975 to 1976.

Kenney had a five-year buyout contract with the Lampoon's publisher, 21st Century Communications. Kenney, Beard, and Hoffman took advantage of this, dividing a sum of $7,000,000 among them. Kenney remained on staff until 1977, when he left the magazine to co-write the screenplay to National Lampoon's Animal House, along with Chris Miller and Harold Ramis.

Kenney died on August 27, 1980, aged 33, after falling from a 35-foot cliff called the Hanapepe Lookout. Police found his abandoned car the following day; three days later, Kenney's body was discovered stuck between two jagged rocks at the bottom of the cliff. His death was Classified as accidental by Kauai police. According Anne Beatts upon Kenney's death, Chris Miller humorously said once that "Doug was looking for a better place to jump from, while he slipped".

Kenney had a small role in Animal House as Delta fraternity brother "Stork," with only two lines of dialogue. Stork's key scene is in the big parade climax, when he sabotages the drum major and leads the marching band down the alley. Kenney selected this role for himself. Produced on a modest budget, National Lampoon's Animal House was, until Ghostbusters in 1984, the most profitable comedy film in Hollywood history.

Chris Miller, co-writer of Animal House, paid homage by naming the main character in his 1996 film Multiplicity Doug Kinney, a variation on, and tribute to, Kenney.

26 years after his death, the book A Futile and Stupid Gesture: How Doug Kenney and National Lampoon Changed Comedy Forever was published, a biography on Kenney and the impact he made on comedy and the people he knew. The book was adapted into the 2018 Netflix feature film A Futile and Stupid Gesture, which stars Comedian Will Forte as Kenney. In the movie, they show Doug's shoes and glasses lying neatly by the otherwise vacant cliffside.