As far as I am aware in the 1790s, Trinity was the only body awarding degrees in Ireland. It admitted Catholics from 1793 onwards (though the Catholic church opposed Catholics attending for about another 100 years). So, if he ignored the church’s instructions – as some students did - Florence could just about have acquired a degree there by 1798 – though the records evidently suggest he didn’t. But if he was genuinely born c 1780, it’s unlikely he’d have qualified by 1798. He’d only have been 18.
According to this article this lady recently became a barrister (advocate) aged 18, but she was the first in England in 600 years to qualify at so young an age, so it clearly wasn’t the norm:
https://www.theguardian.com/law/shortcuts/2013/aug/11/britain-youngest-barrister-gabrielle-turnquest
Florence might have studied in England or Scotland but all the same I’d be surprised if he was fully qualified aged 18. He could also perhaps have studied somewhere like France but most European legal systems are based on the Code Napoleonique, which is quite different to the common law system in use in Britain & Ireland then – and to a large extent even now – so not terribly helpful if you intend to practice in Ireland.
It was at one time possible to qualify as an Attorney without a degree through an apprenticeship called an Articled Clerk but that was a 10 year training process. If Florence’s age was accurate, he doesn’t seem to me to have had time to qualify. Perhaps he may have exaggerated his skills?
There are quite a lot of United Irishmen records in the National Archives in Dublin (Indexed under State papers 620/). You might find more about him there but you would need a researcher to go through them as they are not on-line.
