I imagine it would be a blend of his probable native language in Benin, Yoruba, with the English of 1860s Alabama, Older Southern American English[1]. My best guess for the sound would be to listen to a Beninese speaker of English[2] and imagine it with more of what’s now considered an old-fashioned sophisticated Southern accent, and perhaps less French influence. The closest living relative would probably be African American Vernacular English[3].

It’s important to note that the features of the transcription hint at both his and her accent: she was transcribing the sounds as best she knew how to make someone with her accent pronounce them as he did.

Transcribing his pronunciation of “what” as “whut”, for example, points to the fact that “what” was likely pronounced with [ɑ] in her accent, rhyming with “cot”, but he pronounced it more or less as we do now, rhyming with “cut”. Transcribing “like” as “lak” implies he had /aɪ/ glide weakening (to “ah”, as in “ah do declayuh”) where she didn’t, at least in some contexts—“my” is still transcribed as such, not “ma”. It’s also likely that he didn’t diphthongise vowels, so he’d pronounce “maybe” as something like /meːbi/ instead of /meɪbi/. “Can’t” as “cain” suggests he rhymed it with “cane”, like some AAVE speakers now. And so on.

[1]: https://en.wikipedia.org/wiki/Older_Southern_American_Englis...

[2]: http://www.dialectsarchive.com/benin-1

[3]: https://en.wikipedia.org/wiki/African-American_Vernacular_En...