Well, it's counterfactual history, so it's more about what's unfeasible than inaccurate. With that in mind:

The South realistically could never have 'won' the Civil War in the way described - they had nowhere near the necessary resources and manpower to actually conquer the North. And even if they did, why would they want to? Maybe they'd want to try and annex the border slave states like Maryland and Kentucky that stayed in the Union, and try to force the Union to concede a chunk of the Western territories, but there would be no obvious benefit to the South from conquering the whole North.

Secondly, slavery is reintroduced to the North by a tax that is ameliorated by buying slaves. What, a tax on everyone? This law would be hugely unpopular, even among many pro-slavery people, because many people simply wouldn't be able to afford slaves, in the South as well as the North. And what if the slaveowners didn't want to sell their slaves? Even if they did, there wouldn't nearly have been enough slaves to go around even if each white American owned just 1 slave.

The US had already stopped slave trading half a century before the Civil War, and restarting it would have been a non-starter internationally. By the time the programme refers to the CSA restarting it, Africa was almost completely colonised by European powers, anyway.