This bit o' syntax is easy to get a hold of because it does exactly what you think it does: presents a bunch of grammatical parallels. (Think Julius Caesar's "I came, I saw, I conquered.")

Douglass uses the rhetorical device of parallelism throughout his speech to hammer home his points. Parallelism is a useful tool for piling on evidence, which is what Douglass does.

Check out the bolded phrases:

I will, in the name of humanity, which is outraged, in the name of liberty, which is fettered, in the name of the Constitution and the Bible, which are disregarded and trampled upon, dare to call in question and to denounce, with all the emphasis I can command, everything that serves to perpetuate slavery. (33)

When you can point to any such laws in reference to the beasts of the field, then I may consent to argue the manhood of the slave. When the dogs in your streets, when the fowls of the air, when the cattle on your hills, when the fish of the sea, and the reptiles that crawl, shall be unable to distinguish the slave from a brute, then I will argue with you that the slave is a man! (50-51)

That's the beauty of parallelism. It's clear-cut, but also pretty classy and timeless. It's basically the little black dress of the rhetoric world.