There have been several people with claims to have been slave who had however verify claims have been difficult (lack of records) and most have not held up (many of the claimants would have had to be older than the longest recorded humans to date). The most credible of the group would have been Peter Mills who was born a slave in 1861 and died in 1972, shortly before his 111th birthday. His death was reported in the Pittsburgh Post-Gazette, Sep 23, 1972 (link below). He would have been alive during the entire civil right movement and the passing of the Civil Rights Act of 1968 along with many of other historical events (both world wars and all but one of the Apollo missions).
The two credited with being the last slaves who could recall being slave and had worked on plantations would have been Eliza Moore (1843 - January 21, 1948) and Alfred "Teen" Blackburn (April 26, 1842 – March 8, 1951), the later also among the last confirmed Confederate Civil War veterans. The later would have seen the desegration of the military by President Harry S. Truman's Executive Order 9981 in 1948.