I realize that this is being commonly taught but it's actually incorrect. The various southern accents trace very clearly back to the various British Isles, Scotland and Ireland. The vowel sounds of black Americans were influenced by British, Scottish and Irish-descended southerners.
I thought there was some influence. I know the Irish R’s were dominant in American speech. But I imagine the plantation owners spoke a very high cultured English, and though the vowels were broadened naturally by the distance from England and the more pastoral /rural colony life, I had believed that the slaves’ accented English had an influence in the young children under their watch. Maybe even the rhythmic evenness of American English contrasted with the clipped British of today? Hard to say.
It would be foolish to count out the African influence in language since there was such influence in food and music. And I have seen so many little anglo toddlers here speaking with a Mexican accent our outright fluent Spanish thanks to their nannies.