History has sidelined black stories. Writers can restore them. Just as August Wilson's Century Cycle testified to black lives over the course of the 20th Century, Suzan-Lori Parks gives voice to the slaves that came before them. Father Comes Home from the Wars is a narrative epic of nine short plays – the first three are presented here – that reframes the story of slavery as a core cultural myth like any other. The gesture says it simply: Black Lives Matter. They always have.

Borrowing as much from Brecht as the Ancient Greeks, Parks gives us a hero: a slave named Hero (Steve Toussaint), striving to secure his freedom against the backdrop of America's Civil War. His Texan owner has offered him a deal: fight alongside him with the Confederate army and he can go free. It's a rum deal – to risk death for freedom – but better a shot at life than a life of stoic submission.

Part One builds to a show-down. Years before, bidding to reap the rewards of loyalty, Hero ratted out a runaway, Homer (Jimmy Akingbola). Retribution was swift and harsh: Homer lost his left foot for his efforts, curtailing future attempts, and his every step still rankles as much as Hero's betrayal.

Part Two – best by far – jumps ahead. Hero's owner, the Colonel (John Stahl), has taken a Unionist captain prisoner. Parks sets up a shifting hierarchy: the caged captive freer than the slave; two sworn enemies more united than those fighting side-by-side. Cynically, it's like the classic Frost Report sketch – "I'm a Unionist. I look down on him…" – but Parks gradually, cleverly, complicates the picture. Tom Bateman's Smith isn't all he seems: a private in a captain's coat, a white man with black blood. Statuses slip and allegiances form.

By Part Three, Hero returns home; a free man with a new name, Ulysses – not just a Greek hero, but an American General who would become President. His dog Odyssey – ‘Odd-See' on account of cross eyes – precedes him like a Greek messenger. His wife is waiting. So too, is Homer.

Here, as ever, Parks turns over the notions of freedom and subjugation, ownership and obligation. It's in marriage ("my wife") and in old debts. Panting through the poetry, Dex Lee's Odyssey offers a treatise on his various masters, from Hero to God, finding animal freedoms in deferent friendship.

Parks writes with a plainsong poetry; straight-laced statements spoken aloud. It makes for moments of crystalline articulacy, elegant testimonies to the lived experience of slavery, but at the same time, her play lacks dramatic clout. Though Toussaint stares blankly ahead – privately, he might be defiant, broken or daydreaming – almost everything's on the surface. On this side of the Atlantic, removed from ancestral history, Parks words don't reverberate as they might. For all the plays' purpose, their sage, sangfroid manner, they are fables stretched thin over an hour. Three in a row grows mighty tedious.

Jo Bonney's production, transferred intact with a cast of Brits and South Africans, doesn't help a bit. Plays that are all talk, no action need to find charge by other means. They need some shot of reality onstage, so that their words count, here and now. Though Emilio Sosa's contemporary costumes pull slavery into the present, Neil Patel's design is dated and distancing: fake rocks on a fake desert floor, fake rabbits on fake fires. The result is a tableaux vivant: theatre as tapestry. That fits Parks' play in theory, but in practice, deflates it and tedium is the surest way to stop stories counting.

Father Comes Home from the Wars runs at the Royal Court until 22 October.