http://www.umbermusic.co.uk/BTQtexts.htm

Go to that link and scroll down to the section named "The short song set."

In there is the following:

Billy Flynn (words: trad. tune: B.Brown)
            
Has anyone seen my poor Billy Flynn?
Has anyone passed him by?
It's no joke, his nose is broke,
And one eye is in a sling.
As he hops upon his wooden leg -
And the thought of it makes me cry –
'Cause he leaves round holes
in the mud where he goes
that's what you can tell him by.


I'm guessing that that's all there is, but that's a guess.