A good summary (as usual) in Wikipedia under "Clare de Kitchen" ... a couple of excerpts: "Musicologist Dale Cockrell sees echoes of European mumming traditions in "Clare de Kitchen". In traditional mumming plays, the participants first entered a private household. One mummer, usually with a broom and sometimes with blackened face, would then clear an area and declare the space to now be public, for the use of the players. ... The line "I wish I was back in old Kentuck" is one of the earliest examples of "I wish I was in" from blackface minstrelsy. This line eventually became the famous "I Wish I Was in Dixie" in 1859. ... An alternate set of lyrics, sung by Thomas D. Rice in the mid-1830s, may reflect the input or influence of American blacks. This version features animal characters and trickster figures triumphing over larger animals in the same way that such figures do in African folktales."
It was clearly in oral tradition before the minstrel shows got ahold of it. Andrew Kuntz has some very good background, appropriate for our period, in the Fiddler's Companion. Scroll down CIA-CNU alphabetical directory to entry for "Clear the Kitchen."
CLEAR THE KITCHEN. American, Song tune and Reel. D Major. Standard. One part.For an Irish tune possibly related to "The Gray Cat Kittened in Charley's Wig," look up "CAT THAT KITTLED IN JAMIE’S WIG, THE" in the CAT - CAZ directory and scroll down past CAT AND THE BACON, THE (An Cat Agus an Bagun), the CAT CLUMB UP THE PLUM TREE SCHOTTISCHE and other cat songs.
A bull‑frog dress'd in soldier's clothes,
Went out in the field to shoot some crows.
The crows smell powder and fly away,
That bull‑frog mighty mad that day. (Ford)
Fiddler and musiciologist Paul Tyler has discovered an account by one Joseph Hayes, born in 1786 in Pennsylvania, who moved from that state down the same Ohio river to settle in Lawrenceburg, Indiana. Late in his life he dictated memories of frontier life from circa 1810, including an account of dancing after corn-huskings. Hayes writes that at these events "in one corner would be seated the fiddler delving way with fingers, elbow, cat-gut and horse-hair, to the joy of all around - The pieces of music mostly called for, were 'The gray cat kittened in Charley's wig,’ 'Captain Johnston', 'Buncomb' &c. the whole ending in a jigg called 'Clear the kitchen'.” The minstrel-dialect title “Clar de Kitchen” appears in Howe’s Musician’s Companion, Part 2, published in 1843. Additional verses in Ford (1940, pg. 407). Ford (Traditional Music in America), 1940; pg. 105.