John Laband is the major academic-bridging-popular authority on Zulu kingship and the early kingdom, although others have written important works recently, and some metadiscussion like Dan Wylie's Myth of Iron: Shaka in History (2006) are still valuable. There are others who work on a variety of aspects of the kingdom, but if you need the overview, Laband is your best bet. His most recent book is The Eight Zulu Kings (2018), which of course starts with your focus. Contextually, Rope of Sand (1998, in the US as Rise and Fall of the Zulu Kingdom) still stands up really very well. I suppose one might look at the relevant chapter (Wright's "Turbulent Times") from the Cambridge History of South Africa (v. 1, 2009), but it frankly is dense with detail that is not accessible to a general reader in the way Laband's work tends to be. He [edit 2: Laband] pays great 0attention to the internal politics of kwaZulu and, of course, knows the relevant languages.

I'm still a fan of Norman Etherington's The Great Treks and the Transformation of Southern Africa 1815-1854 (2001) as an entry to the so-called 'mfecane wars' but he deals much less with Zulu matters specifically, preferring a broad reinterpretation of developments in the heart of the subcontinent.

[edit: fixed italics, d'ohhhh] [edit 2: clarification at end of para 1]