Here's a good dissertation, if not a book, about Latin America's Cold War as a whole. Allende and Chile make up a major segment of it. I prefer works that emphasize dynamics in the Southern Cone, in keeping with my view of the Cold War, as well as Allende's administration as a whole rather than just the coup itself. There's more to history than Washington and Moscow.

https://www.utexas.edu/lbj/archive/osap/uploads/file/Brands_Dissertation.pdf

If you want to look at it from the POV of the Soviet KGB, the Mitrokhin Archives would be useful. As for the American POV, you can look at declassified State Department documents. Any book on Nixon or Kissinger that covers the period (Dallek, Isaacson) inevitably will have a section on this as well, although you've got to be careful about the political slant of some of them.