I'm not surprised you can't find it here; beside references to the historical event itself, the only reference to a song of that name I can find anywhere is in a songsheet at the Library of Congress  America Singing: Nineteenth-Century Song Sheets  site:

:

The flow'ry Shannon side.  Air: Burning of the Henry Clay.  H. De Marsan, Publisher, 38 Chatham Street, N. Y.

Which is no direct help, but at least may provide an alternate line for enquiry.