Castlebay has recorded a version of Ettrick (via Anne Dodson) on our album "Ae Fond Kiss".Although Archie Fisher sings a version of it, Lady Scott did write a tune for it. This song is listed as "When first we rode down Ettrick", on page 46 in Thirty songs by Lady John Scott, Patterson & sons 1910
https://archive.org/details/thirtysongs00scot

Also this
from SONGS AND VERSES BY LADY JOHN SCOTT
Printed by R. and R. Clark, Limited
EDINBURGH : DAVID DOUGLAS 1904

No one was more humble about her own
performances. She was so unfeignedly pleased
if any one liked a song she had made, and she was
always willing to give it away. Her dislike of
publicity was the reason so few have ever been
printed. After the Crimean War she gave " Annie
Laurie " and several others to Lonsdale to publish
for a bazaar for the widows and orphans of soldiers
who had been killed. Some more were published
later for another charity, but most of her songs are
still in the original MS. She copied with her own
hand a complete set for her lifelong friend, the
late Lord Napier ; and this collection lent to me
by the Dowager Lady Napier has been of the
greatest help in putting together the volume of
Lady John's music which I hope to bring out very
shortly.

BTW, it is NOT about the battle of Flodden. Lady Scott suffered the death of many friends and family- this song is most likely about her beloved husband who died in the winter of 1859.

best- Julia