There are several Sligo musicians with the surname "Flynn" mentioned in Seamus Tansey's book "The Bardic Apostles Of Inisfree", including accordion player Sonny Flynn. I've had a quick "skim" through them but didn't find any mention of any John Flynn in any of the biographies composed by the estimable Mr. Tansey, including Sonny Flynn's. I can't help but wonder if "John" Flynn and "Sonny" Flynn might not have been the same person, but that's sheer supposition on my part. I'll have a closer read through the biographies - and also check Tansey's 2nd volume to see if the name comes up anywhere. Bernie Flaherty's excellent tune collection "The Trip To Sligo" contains brief biographies of many Sligo players - I'll see if the name comes up anywhere there as well.
There are various organisations specialising in the traditional music of Sligo who I'm sure could be of more assistance than an Irish music fanatic from Aberdeen, but I'll do my best.
Good luck in your quest, Kenny