The initial 'Ka' rhymes with 'sky,' the 'lin' with 'bean,' and the 'a' is like what the dentist says when he/she tells you to say 'ah.' Mostly it's the first syllable that's different with these guys than the other versions I hear.
I imagine this is telling as to where they come from. Their name is the 'Ural Cossacks,' if that helps. Is the pronunciation like that in the Urals? Or of the Cossacks? Or something else?