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I’ve read in a few places that regimental doctrines exist in Kill Team for Astra Militarum, however I cant seem to find any reference to these in the core rule book. Could someone please fill me in on where I can find these? If they’re not in the Core book, are they part of the core game?

It's in the Elites book.

They are part of the Elites expansion.

Technically not part of the core game. However its dependant on your local a meta. A lot of places are treating Elites as a "mandatory expansion" due to all the options it added (like making custodes playable)