National Archives and the National Maritime Museum.
The Admiralty used to maintain a list of officers blacklisted from further appointments - I'm damned if I can remember what its called but it's in the National Archives. Its about the right time period for this Flynn character to be in it.
He's not in O'Byrne's Biographical Dictionary of Naval Officers - I looked in my copy. But that's not entirely surprising as O'Byrne wrote and asked for biographical details.
You could try grubbing through the appropriate Navy Lists of which there are runs of hardcopy in Kew, and in Portsmouth Public Library (upstairs, take id). The account of his prior 'legitimate' services must have come from him and is, I suspect, not to be trusted. There might be more in The Times archive, probably accessible to you via your County library card.