He was born on 28 January 1890 in Woollahra, the eldest son of Sir Philip Whistler Street and his Melburnian wife Belinda Maud. He attended Sydney Grammar School and Sydney Law School, winning scholarships in law. World War I began while he was visiting family in England and on 29 September 1914 he was commissioned to serve with the Duke of Cornwall's Light Infantry in France. His elder brother Lieutenant Lawrence Whistler Street, a fellow Sydney Law School student, enlisted before him and was sent to fight in the Battle of Gallipoli, where he died serving the Allied forces at age 21. Lawrence had volunteered for national service in August 1914, making him one of the earliest of his generation to do so. Sir Kenneth named his son Sir Laurence Whistler Street in his brother's honour. Street was appointed Lieutenant, 18th Infantry Regiment, in December 1915. He served in the Adjutant General's Department, Army Headquarters, Melbourne, and was promoted temporary Captain in September 1917. Although he had been admitted to the New South Wales Bar Association on 12 March 1915, he did not practise until he ceased full-time military duties in December 1919.
Juridicial career
Between 1921 and 1927, Street lectured part time at Sydney Law School. Meanwhile, he continued his career in the Militia as a legal staff officer and rose to the rank of Lieutenant-Colonel. He was a considerable scholar in and beyond the law, being an authority on the writings of Pepys and an accomplished Latinist. Street enjoyed a wide general practice and would have taken silk but for his appointment to serve on the reconstituted Industrial Commission of New South Wales from 16 December 1927. He was elevated as a judge of the Supreme Court on 7 October 1931. He thus joined the bench of which his father was then Chief Justice, the first and only such case in Australian history. In 1949, as senior puisne judge, Street acted as Chief Justice when Sir Frederick Jordan died. Confirmed in that office from 6 January 1950, he was sworn in on 7 February, thus becoming the second of three consecutive generations of the Street family to serve as Chief Justice of the Supreme Court and Lieutenant Governor of New South Wales.
Members of the Street family have been prominent in law, politics, civil service, and the military, especially in Australia and in the state of New South Wales, since the 19th century. The progenitor of the Street family was Sir Thomas Street, Chief Justice for Brecknock, Glamorgan and Radnor in 1677, and Baron of the Exchequer as of April 1681. Street was married to Lady Street, a prominent suffragette and human rights activist. They had four children including Commander Sir Laurence Street,, who also attained the position of Chief Justice. Sir Kenneth's daughter Philippa married the Australian Test cricketer and journalist Jack Fingleton,.