Kendall was the youngest of the eight children of Charles Kendall, a commercial traveller, and his wife Hannah Eltringham. He was born on 15 November 1856 in Mile End, London.
In 1885 Kendall became Bishop Berkeley Fellow at Owens College, Manchester, by then part of the federal Victoria University. In 1887 he was appointed an Assistant Lecturer in Geology there. In 1889 Kendall moved to Stockport Technical School as a part-time Lecturer in Natural Sciences.
By 1891 Kendall was also lecturing part-time at the Yorkshire College in Leeds. The Yorkshire College became the University of Leeds in 1904. The university awarded him the degree of MSc in 1905 and in the following year appointed him Professor of Geology. Kendall retired from his chair as Emeritus Professor in 1922.