Green River is a tributary of the Ohio River, thus the flow of the current is generally from east to west.
It appears to flow unimpeded from Green River Lake near Campbellsville and Hatcher in Taylor County.
From Taylor County it flows into Green County and then into Hart County.
Approximate road miles from where the body was discovered to the outflow at Green River Lake is 40-50 miles by my Google maps reckoning. "Crow flies" distance is shorter, of course.
Distance in river miles from the lake outflow will be greater as the Green River meanders considerably.
Green River Lake:
http://parks.ky.gov/parks/recreationparks/green-river/
Green River in Hart County:
http://fw.ky.gov/Education/Pages/Green-River---Hart-County.aspx
Additional information on the Green River from KY Fish and Wildlife:
http://fw.ky.gov/Pages/search.aspx?terms=Green+river&affiliateId=FW
Map of KY counties:
http://geology.com/county-map/kentucky.shtml