Also see this paper

http://www.census.gov/prod/2012pubs/acsbr10-18.pdf

and an interactive map

http://blogs.lib.uconn.edu/outsidetheneatline/2014/01/28/gini-index-of-income-inequality-for-u-s-counties/

which says to use ACS table B19083

I'm not sure if this bookmark will work but see the ACS table here

http://factfinder2.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=ACS_12_5YR_B19083&prodType=table

Also see this paper

http://agecon2.tamu.edu/people/faculty/wu-ximing/agecon2/public/welfare.pdf

In American Factfinder: Table B19083

I agree it is  a tricky thing to find the data. Especially if you want to get some  time series as well. 1969, 1979, 1989, 1999 data are available directly from census: https://www.census.gov/hhes/www/income/data/historical/state/state4.html

After that for more recent years, I agree with the comments before, that you have to reply on papers and reports: https://www.census.gov/prod/2012pubs/acsbr11-02.pdf

Good luck. 

What Edward Jepson said: Table B19083. However, American Factfinder no longer exists -- you will need to access the data through the US Census site, and it is a navigational nightmare. I recommend using the table number as your search term, since "inequality" will not pull up county-level data. Good luck! (It's almost as if someone *wants* to make this data difficult to obtain... Nah, that's just crazy talk...).

Greetings... CountyHealthRankings by the Robert Wood Johnson Foundation has some 80% income, 20% income, and an income ratio - that I presume would do what you need. I'm not sure on their sources at the moment, but the details are on the last tab of the Excel sheet or in their documentation. Feel free to look here:

https://www.countyhealthrankings.org/explore-health-rankings/rankings-data-documentation

Then click on the data file located called: 2019 County Health Rankings National Data

American Factfinder is still functioning until June 2020: https://factfinder.census.gov/faces/nav/jsf/pages/index.xhtml

BTW, Nick Jorgensen is right about using the data.census.gov website: type in the table 19083 and then you can select your geography.