Here is a link to that registry. It probably would not take all that long to scroll through the whole lot, but easier if you could take a guess as to what the first letter is!
International Burgee Registry
In any event, a burgee would typically signify membership of an organisation, and in that case it would not be appropriate to fly it if you are not a member of the particular entity.
If you want a burgee to fly that is a conversation piece as well, you could try this one, and like me end up as a card-carrying Vice-Commodore:
https://www.sicyc.com.au/