Brinkley was born in Custer, Oklahoma on September 10, 1917, and graduated from the University of Oklahoma in 1940.

Brinkley was an officer in the United States Navy during World War II, where he served in Europe and the Pacific, primarily in public relations duties.

Afer graduating from the University of Oklahoma in 1940, Brinkley went on to work for The Daily Oklahoman in Oklahoma City, Oklahoma. Afterwards, Brinkley was a reporter for The Washington Post from 1941 to 1942 and 1949 to 1951. He was also a staff writer, correspondent and assistant editor and for Life magazine from 1951 to 1958. Brinkley was also a member of the National Press Club until his death in 1993.

1940s

In 1948, after his tenure as an officer in the United States Navy during World War II, Brinkley wrote and published his first novel, Quicksand.

1950s

In 1954, Brinkley wrote his only non-fiction book, The Deliverance of Sister Cecelia, a biography of a Slovakian nun based her memoirs as recited to him. The novel was later adapted into an eponymous episode of Climax! in 1955. In 1956, he went on to write the best-selling novel and perhaps his most prominent work, Don't Go Near the Water, a comedy about United States Navy sailors serving in the South Pacific during World War II. Don't Go Near the Water would later be adapted into film by Metro-Goldwyn-Mayer as Don't Go Near the Water. Don't Go Near the Water was released in theaters across the United States in 1957 and became both a critical and commercial success.

1960s

In 1961, Brinkley wrote and published The Fun House, a comedy novel set in the offices of a picture magazine, similar to that of Life. The following year, in 1962, Brinkley wrote and published the novel, The Two Susans, which was followed in 1966 by The Ninety and Nine, a novel detailing life on board a United States Navy LST during World War II.

1970s

In 1971, Brinkley moved to McAllen, Texas and would live there until his death in 1993. Throughout the 1970s, Brinkley only wrote one novel, Breakpoint, which was published in 1978.

1980s

Breakpoint was followed by Peeper, a comedy novel about a voyeur in the small Texas town of Martha, Texas, near the Rio Grande river. Peeper was written by Brinkley and published in December 1981. In March 1988, Brinkley wrote and published his last work, The Last Ship, a post-apocalyptic fiction novel dealing with the sailors of a United States Navy guided missile destroyer which survives a global nuclear war.

After suffering from a major depressive disorder for over several years, Brinkley committed suicide at the age of 76 from an overdose of barbiturates on November 22, 1993. He died at his home in McAllen, Texas, near the Gulf of Mexico.

Novels

• Quicksand (1948)
• Don't Go Near the Water (1956)
• The Fun House (1961)
• The Two Susans (1962)
• The Ninety and Nine (1966)
• Breakpoint (1978)
• Peeper (1981)
• The Last Ship (1988)

Non-fiction

• The Deliverance of Sister Cecelia (1954)