I have never heard of this song before but the lyrics are a perfect fit for "MOLLY BAWN" an irish song about a guy pretending to join the British Army. The tune used by the 7th Cavalry was "Garryowen for Glory" or "Garryowen In Glory", definitely not the music for this song.
The first verse of Molly Bawn goes Oh come listen to my story Molly Bawn
For I'm bound for death or glory Molly Bawn
For I've listed in the army
Where no more your eyes can charm me
For they would kill me as they charm me Molly Bawn.
Sgt Flynn would of course come in in the place of Molly Bawn - I know the tune but don't know how to put it on the net, I'm sure someone will be able to do it.