In 1861 he became an assistant at the University of Copenhagen Botanical Garden.
From 1882 to 1889 he was teacher in the Monrad'ske Kursus (a course named in honour to the Danish prime minister Ditlev Gothard Monrad) at Danmarks Lærerhøjskole (Denmark's Teacher's College).
From 1876 to 1883 he was assistant at the chemical laboratory of Sigfred Frederik Edvard Valdemar Stein.
Kiærskou published the scientific descriptions of several plant taxa from the families Lythraceae and Myrtaceae, in particular from Spain and Brazil.
Together with Samsøe Lund he wrote a monograph about the cultivated forms of the cabbage, the beet, and the rapeseed.