Old-Fashioned, Elevated, Plain, Personal, Biblical
Although Douglass's language may seem a bit stilted to us today, his style is usually pretty straightforward. He wants you to understand him, so he doesn't write long or complicated sentences, and he tries to speak informally, as if it were just you and him.
Still, he does sometimes use a kind of elevated language, and parts of the book can be a bit difficult. It might be that he's emulating the style of the King James Bible, one book that almost all of his readers would be familiar with. And he also might be showing off a little, since he had to fight so hard to learn how to read and write.
For example, this is how he describes Aunt Hester being whipped:
I remember the first time I ever witnessed this horrible exhibition. I was quite a child, but I well remember it. I never shall forget it whilst I remember any thing. It was the first of a long series of such outrages, of which I was doomed to be a witness and a participant. It struck me with awful force. It was the blood-stained gate, the entrance to the hell of slavery, through which I was about to pass. It was a most terrible spectacle. I wish I could commit to paper the feelings with which I beheld it. (1.8)
Words like "exhibition" and "spectacle" remind us that, even though Douglass is remembering something he saw as a child, he's a well-educated adult now. He seems to want to show us that his hard-earned education was a success. But he is also is aware of the limitations of language. At the end of the quote, he reminds us that no matter how powerful a writer he might be, language cannot quite capture the trauma of the experience.