In May 1674 he was acting as tutor ("governour") to Lord Bruce at Glasgow College, where he lodged for some time with Gilbert Burnet.
In the same year he was offered by Sir Robert Milne of Barntoun, provost of Linlithgow, the mastership of the school there, and eventually accepted in 1675.
[1] In John Penney's History of Linlithgowshire and George Chalmers's Life of Ruddiman, Kirkwood is spoken of as the leading grammarian of his day.
At the suggestion of Lord Stair, president of the court of session, he was consulted by the commissioners for colleges and schools as to the best Latin grammar to be used in Scotland.
In 1695 he produced Grammatica Despauteriana, cum nova novi generis Glossa: cui subjunguntur singula primæ Partis Exempla Vernacule Reddita.
Many years later he published The History of the Twenty Seven Gods of Linlithgow; Being an exact and true Account of a Famous Plea betwixt the Town-Council of the said Burgh, and Mr. Kirkwood, Schoolmaster there.
The work contains details of the social and religious state of affairs during the contention for supremacy between the Presbyterian and Prelatic parties.