I have a large Kain family in my tree which goes back to a William Kain b. 1781 in Ireland. He bought his two children to Campsie in Scotland where they raised large families. Don't know date of arrival but they are in the 1851 census in Campsie.

My surname atlas based on the 1881 census shows the name clustering around Dumfries/Galloway and also Lancashire which I interpreted as further proof of the Irish origin.