'Kin' is outdated word. In terms of everyday usage, you could probably call it archaic.
But words rarely curl up and die completely : even if we stop using them on a day-to-day basis, they still carry on in isolated pockets. Here we have a few examples of those pockets : fixed phrases and jargon ( as in the fossilised 'kith and kin' and the legal term 'next of kin') as well derivatives such as 'akin to' 'kindred' ( e.g. 'a kindred spirit), academia (as in Irena's example), and regional dialect (often vilified - which is why Madame S. Pierre disapproves).
As you know, much of my knowledge of US culture comes from a misspent youth watching old episodes of the Beverly Hillbillies. When I think of 'kin' in an American context, this is what springs to mind:
Well the first thing you know ol Jed's a millionaire
The kinfolk said "Jed move away from there"
The choice of word is deliberate - it sounds old-fashioned and folksy. I even seem to remember Grandma talking about family as 'kin'.
In British English, we have all the examples above, including the fairly common fixed phrase 'next of kin'. 'Kin' meaning 'relatives' may still exist in some regional dialects, but I've never heard it.