Many of Burns's poems *were* songs -- that is, he intended them to be sung, and had tunes in mind. You can find them all (tunes included) in _Burns: Poems and Songs_, James Kinsley, Ed., Oxford Univ. Press, 1969.

I have never been able to find out if Kipling had tunes in mind, but he called many of his poems "song" or "ballad" in their titles, and many of them have been set to music again & again, and sung in music halls, parlors, and elsewhere. Peter Bellamy, Roberts & Barrand, and Leslie Fish, whose efforts in that way many of us have enjoyed, are latecomers.