I've long been fascinated by the KoK but never come across a comprehensive history. Recommendatioms with any scope and angle are welcome (whole era, focus on triangle trade, as part of a broader West African history, etc).
There has been a good deal written about the kingdom, and there is some very interesting research coming to press right now, products of the KongoKing archaeology project. Of the two listed there, The Kongo Kingdom; origins and dynamics of an African polity will be much more historically focused and gives a broad overview of the kingdom's history.
The scholars who contribute to the book, John Thornton, Linda Heywood, Cecile Fromont, Igor Matonda, are eminent historians of the Kongo kingdom and Kongo diaspora in the Americas. Meanwhile, Pierre de Maret, Bernard Klist, Els Cranshof and Nicolas Nikis are well known archaeologists who were intimately involved in the project. Koen Bostoen is a linguist who co-directed the KongoKing project with Pierre de Maret.
Also, UNC Duke and University of Florida co-hosted a conference called the "Kongo-Atlantic Dialogues" which has been filmed and uploaded to youtube by Benjamin Hebbelthwaite
If you are interested specifically in Kongolese in the Slave trade, Linda Heywood's Central Africans, Atlantic Creoles and the Foundations of the Americas, 1585-1660 and the similarly titled Central Africans and Cultural Transformations in the American Diaspora and there is also the chapter "Kongo and Dahomey, 1660–1815: African Political Leadership in the Era of the Slave Trade and Its Impact on the Formation of African Identity in Brazil" in Soundings in Atlantic History she co-wrote with John Thornton.
John Thornton has also written extensively about the Kongo Kingdom and the Kongolese diaspora in the Americas. You might start with his book The Kongolese Saint Anthony about the Antonian movement in Kongo from 1684-1706 which sought to end a cycle of civil wars and related slaving. Africa and Africans in the making of the Atlantic World gives a broader continental scope, but his expertise with Kongo means he gives the kingdom a good deal of attention. He has also written more specific journal articles and chapters, including one about Kongo urbanism in Africa's Urban Past [though the articles coming out of the KongoKing project will alter some of his conclusions].
Hope this helps!