1777... Although that probably requires ending the US rather than slavery.
What is the earliest possible date that slavery would end?
Late Revolutionary War.
Washington backs his buddy Laurens' idea, and when Congress does its inevitable repeated betrayals (not paying soldiers, no retirements, etc), Washington has Congress emptied long enough to get Laurens's idea (and a few other thoughts of Washington's) made into law...and only then allows the Congress to come into play again.
US loses war of independence. Britain outlaws slavery in the Empire in the 1830's. Bam, no more slavery.
Sooner or later, they probably would.If Britain wins the war of independence, they will not outlaw slavery. Britain could out law slavery because they could get thier slave cotton without having to keep the slaves. If the cotton colonies are still part of the Empire, Britain will not outlaw slavery.
The Boll Wevil in 1916 would probably kill slavery.