The tune is quoted in Bronson from Albyn's Anthology, vol.I (1816), p. 78. Bronson was rather suspicious of the authenticity of the melody, and in particular of its second strain; but printed it with reservations. It's one of those I've made a midi of for eventual inclusion in the DT. For now, you can hear it via the South Riding Folk Network site:

Kinmont Willie (midi).