The song was written about the war of 1812, not the revolutionary war.

As the wikipedia article points out, during the revolutionary war most of the black Patriots were recruited from the north already as free men of color and were at the time lionized for their actions (albeit in predictably racist terms) - and abolition would take over the north quite quickly afterwards (most having some form of abolition well before 1800). The first continental congress also banned the import of slaves in 1774 (though abolitionists cheered it at the time and rightly so, it should be said that this was primairly a method of applying economic pressure to the british), and would set up the civil war by doing so.