The Funky Butt was more of a style of movement than a dance. The idea was thus: A women would raise her skirt to show off her petticoat or what have you and suggestively move her hips. Coot Grant says: 'While she raised her skirt she would grind her rear end "like an Alligator crawling up a bank".
The word funky was around in the 1920s to refer to an obnoxious smell, especially referring to a person who smelled bad. Anne Hegerty wrote “At least a hundred years ago there was a dance hall in New Orleans whose official name was Kinney’s Hall or McKenna’s Hall (sources differ) but which was known to local jazz and ragtime musicians and dancers as Funky Butt Hall (ie: Smelly Bottom Hall). Buddy Bolden
used to play there. Buddy Bolden became the first of many giants of jazz and was a powerful cornetist who played every type of music all over the city and was best known for his hot music in the funky butt night club he was the most famous musician in New Orleans and best loved in Storyville the infamous red light district and his career ended there in 1906.
The Funky Butt is still done in many dances today and as you could probably tell became very popular within the Burlesque community. There is also a newer adaption called the Funky Booty Butt Dance that is basically the same idea but with a little more alternating, circular arm choreography.