Kinneir was born in Hampshire in 1917. He studied engraving at the Chelsea School of Art from 1935 to 1939. After World War II Kinneir was employed as an exhibition designer by the Central Office of Information. He next worked for the Design Research Unit, and then opened his own practice in 1956. He also taught part-time at the Chelsea School of Art.

Kinneir's first big commission was the design of the signage for Gatwick Airport. He chose one of his students at Chelsea, Margaret Calvert, to assist him. When Sir Colin Anderson, the chairman of the P&O Line shipping company read about the Gatwick signage, he chose Kinneir to design a baggage labelling system for P&O. 

In 1957 a government committee was formed to design signs for the new British motorway network, and afterwards to review signage on all other British Roads. The objective was to produce signs that could be read at speed. 

Jock Kinneir was commissioned as the designer. 

In 1964 he made Margaret Calvert a partner and renamed his practice Kinneir Calvert Associates. They devised a code of carefully chosen shapes and colours that largely complied with the protocol proposed by the 1949 UN World Conference on Road and Motor Transport. Kinneir and Calvert developed a new typeface, based on Akzidenz Grotesk. This typeface was later named Transport. It was first used for the Preston By-pass in 1958. Kinneir and Calvert later completed other design projects. They introduced the Rail Alphabet typeface for British Rail and worked for hospitals, the Army and for other airports. 

Kinneir taught at the Royal College of Art and was head of the graphic design department for a while. The original road sign maquettes (models) produced by Kinneir and Calvert for a presentation to the Ministry of Transport are now held at the St Bride Library in Fleet Street.