What about the role of the CIA in a democratic society? Is that an oxymoron?

You could imagine a democratic society with an organization that carries out intelligence-gathering functions. But that's a very minor part of what the CIA does. Its main purpose is to carry out secret and usually illegal activities for the executive branch, which wants to keep these activities secret because it knows that the public won't accept them. So even inside the US, it's highly undemocratic.

The activities that it carries out are quite commonly efforts to undermine democracy, as in Chile through the 1960s into the early 1970s [described on pp. 91-95]. That's far from the only example. By the way, although most people focus on Nixon's and Kissinger's involvement with the CIA, Kennedy and Johnson carried out similar policies.

Is the CIA an instrument of state policy, or does it formulate policy on its own?

You can't be certain, but my own view is that the CIA is very much under the control of executive power. I've studied those records fairly extensively in many cases, and it's very rare for the CIA to undertake initiatives on its own.

It often looks as though it does, but that's because the executive wants to preserve deniability. The executive branch doesn't want to have documents lying around that say, I told you to murder Lumumba, or to overthrow the government of Brazil, or to assassinate Castro.

So the executive branch tries to follow policies of plausible deniability, which means that messages are given to the CIA to do things but without a paper trail, without a record. When the story comes out later, it looks as if the CIA is doing things on their own. But if you really trace it through, I think this almost never happens.