The conditions of Haiti at the time of the revolution were quite a bit different than those in the United States at the same time. Haitian/African slaves outnumbered white people in Haiti 10 to 1 (slaves made up about a third of the population of the confederate states going into the Civil War). The French Revolution and the Napoleonic Wars led to a muted response to the revolt from the French military, as they were focused on matters they deemed more pressing. There was a large outbreak of yellow fever, that killed a lot of the white French in Haiti in the midst of the revolution. And even given that, close to half of the Haitian slaves were killed during the revolt. It was a bloody mess. They did win independence though.
A lot of leaps of logic would be needed to set up a similar scenario in the United States, given differences to demographics, political interests, etc.
Granted, government sanctioned slavery persisting in the US up until 2017 is far-fetched as well, even if the confederates somehow won the civil war. That was my major issue with the Underground Airlines. A US/Confederate state-branded apartheid system, as seen in South Africa in the second half of the 20th century? Sure. Actual chattel slavery in a post-industrial, post-globalization United States? International relations would have forced an end to that, even if they turned a blind eye to civil rights abuses that are inherent in racial caste systems.
EDIT: I remember seeing that we are getting a show where emancipated slaves were given ownership of land (a couple of states?) and self-determination as reparations for slavery. I think that is a more interesting concept. It requires you to buy into a mass expropriation of land and property from many wealthy families at the conclusion of the civil war, but similar things have been done in history.
