He was born in Chobham, Surrey to soldier William Henry Kendall of the Royal Horse Artillery, and his second wife Rebecca Pickering. James attended the local village school and then from 1900 Farnham Grammar School. In 1907 he went up to Edinburgh University graduating both Bachelor of Science and Master of Arts in 1910. In 1912, with the help of a scholarship he left for the Nobel Institute for Physical Chemistry in Stockholm to work with Arrhenius on electrolytes.
In 1913 he accepted the position as Professor of Chemistry at Columbia University, New York. He also served in 1917 as a Lieutenant Commander in the United States Naval Reserve, acting as Liaison Officer with Allied Services on Chemical Warfare.
His candidacy for the Royal Society of London in 1924 read: "Distinguished as an investigator in physical and general chemistry. Has published since 1912, partly with collaborators, over sixty papers in Proc Roy Soc, Journ Chem Soc, Phil Mag, Journ Amer Chem Soc, Journ Phys Chem, etc, dealing with the following subjects: - 'Mechanism of the Ionisation Process'; The Problem of Strong Electrolytes'; 'Correlation of Compound Formation, Ionisation and Solubility in Solution, and in Fused Salt Mixtures'; 'Prediction of Solubility in Polar Solutions'; 'Stability of Hydrates and other Additive Compounds'; 'Viscosity of Binary Mixtures'; 'A Method for the Separation of Rare Earths and of Isotopes."  He was elected a Fellow (FRS) in 1927.
In 1929 he was elected a Fellow of the Royal Society of Edinburgh. His proposers were Sir James Walker, Alexander Lauder, George Barger, and John Edwin Mackenzie. He served as the Society's Secretary 1933 to 1936, General Secretary 1936 to 1946, Vice President 1946 to 1949 and President 1949 to 1954.
In 1938 Kendall was invited to deliver the Royal Institution Christmas Lecture on Young Chemists and Great Discoveries.
He retired in 1959 and died in Edinburgh in 1978. He had married Alice Tyldesley of British Columbia in 1915 who died in 1955. He was survived by his second wife Jane Bain Steven and children from his first marriage, including James Tyldesley Kendall FRSE.
He wrote and co-authored several books including:
- At Home Among the atoms (1929)
- Smith's Introductory College Chemistry (revised 1938) Appleton-Century, New York
- Breathe Freely! The Truth About Poison Gas. First published April 1938, reprinted April 1938 and again in 1939 by Camelot Press Ltd London and Southampton
- Young Chemists and Great Discoveries, G. Bell & Sons, London, 1939
- Humphry Davy "Pilot" of Penzance (1954)
- Michael Faraday, Man of Simplicity (1955)
- Campbell, N.; Kemball, C. (1980). "James Pickering Kendall. 30 July 1889 – 14 June 1978". Biographical Memoirs of Fellows of the Royal Society. 26: 255–273. doi:10.1098/rsbm.1980.0007. S2CID 71924273.
- Biographical Index of Former Fellows of the Royal Society of Edinburgh 1783–2002 (PDF). The Royal Society of Edinburgh. July 2006. ISBN 0-902-198-84-X.
- Ross, Shan (24 September 2013). "The Scotsman, 24 September 2013". Edinburgh. Retrieved 8 January 2014.