this nonsense-song won wakean immortality purely for the coincidence with the biblical Esau's hairy arm, impersonated by Jacob with a goatskin, so that Shem and Shaun can symbolically be one side or the other
sheepskin pants (and boots, vests, etc), usually but not always worn woolly-side-in, are still popular in very cold climates, so the song's satire is oddly weak
it's quoted by Boucicault in The Colleen Bawn: 'Enter Myles, singing "Brian O' Linn." Myles: "Brian o' Linn had no breeches to wear, So he bought him a sheepskin to make him a pair; The skinny side out, the woolly side in, 'They are cool and convanient,' said Brian O' Linn."'
Bryan O'Lynn was a gentleman born
He lived at a time when no clothes they were worn,
But as fashion went out, of course Bryan walked in
"Whoo, I'll lead the fashions," says Bryan O'Lynn.
Bryan O'Lynn had no breeches to wear
He got him a sheepskin to make him a pair,
With the fleshy side out and the woolly side in,
"Whoo, they're pleasant and cool." says Bryan O'Lynn. [more]
006.22 "Belling him up and filling him down. He's stiff but he's steady is Priam Olim!"
060.11 "Brian Lynsky"
110.02? "That was just where Brien came in."
148.36 "Lyon O'Lynn"
328.02 "Bruin O'Luinn" (rhyming slang Brian O'Linn: gin?)
017.11 "with his woolseley side in... did Brian d' of Linn"
070.07 "the Lynn O'Brien, a meltoned lammswolle"
275.01 "from Bryan Awlining! Erin's hircohaired culoteer."
373.16 "Bruni Lanno's woollies on Brani Lonni's hairyparts"
035.13 "carryin his overgoat under his schulder, sheepside out"274.32 "a broken breached meataerial"
338.18 "with his soilday site out on his moulday side"
507.06 "with the coat on him skinside out"
529.32 "this fancydress nordic in shaved lamb breeches"
the 7thC French king Dagobert is ridiculed in song for absentmindedly putting his culottes (knee-breeches) on backwards
cf 'Le bon roi Dagobert A mis sa culotte à l'envers' (Good King Dagobert Has put his culottes on backwards)
VI.B3.92: "Dagobert educated at Slane (cf Brian O'Linn)"
035.12 "still berting dagabout"
274.29 "vaunty years Dagobert is in Clane's clean"
394.18 "Lally of the cleftoft bagoderts"