Many thanks peterm and I'm sorry if my clue has turned out to be controversial. Your parsing is spot on:
Although I've never heard the term used in Glasgow I had heard it used in my hometown of Stirling many years ago. That alone would have been too local to justify its use here but if anyone would care to look in Chambers;
ken²: a house, esp a disreputable one.
Hope this helps.
Cheers peterm, "Farty Towels" timeless.