Whoever indexed the 1840 Livingston County, Kentucky census for ancestry.com confused a lot of researchers. According to ancestry.com, there were three districts in 1840 Livingston County - Salem, Smithland and Swingslow - but if you enlarge the name written along the left side of the page for the last district, it is evident that it says Livingston and not Swingslow. I've reported this error to ancestry.com in the past and just reported it again. Let's hope it gets corrected this time.
Bottom line - there was no Swingslow district. The word should be Livingston.