A couple of slight misconceptions here that might help your understanding. Kidnapping is probably not an accurate description of the slave trade especially in south and central Africa. Entire societies developed and adapted themselves in central Africa to the acquisition and transportation of slaves to the coast. While often raiding was a method for acquiring slaves, this was a mercantile pursuit for the majority of people (European and African).

I'm not quite sure what you mean by "American" in your question. If by the "American Slavery Machine" you mean the slave trade and slavery in the USA, a very small percentage of slaves came from outside west Africa. However, slaves very much were transported to the south, Portuguese speaking Americas from Angola and the Congo. Comparatively the slave trade to the USA was small part of a much a bigger slave trade to the America's and the Caribbean. The Portuguese slave trade was actually much bigger than the trade to America.

There is an very comprehensive book on the topic of the Portuguese slave trade by Joseph Miller called Way of Death: Merchant Capitalism and the Angolan Slave Trade, 1730–1830. Miller covers the entirety of the Portuguese slave trade, from how slaves were acquired in the interior, transported to the coast and the exported to South America. He also manages to detach from a cold capitalistic view of the trade at points to give the human perspective of the slaves. If you're really interested in the topic I recommend reading it. If you'd like to hear more about the Portuguese trade I'd be happy to write about it, but it's not really directly related to your question.