Finlay was educated at the Glasgow Grammar School and briefly studied at the University of Glasgow and was elected its Rector in 1819. In 1820, unfounded rumours spread around the university that he was building up a motion to disallow student voting at rectorial elections. In the resulting student campaign Finlay was defeated in the re-election by Francis Jeffrey. He however later served as Dean of Faculties between 1839 and 1840.
