Who does Patricia work for?

The clear implication is that she's a double agent, working for the Soviet Union.

We know from the film script that she was involved in "Operation Chaos" (e.g. that she's a CIA agent) but her actions; killing CIA agents, giving away their secrets, etc would strongly suggest that she's either for the Soviets. There's mention of a "mole" earlier in the film. It's almost certain that it's her.

Her motivations and reason for turning (e.g. whether it's for money or for philosophical reasons) are not disclosed in the film but it's pretty clear that she's been working as an undercover agent for a considerable time without a handler and is disillusioned with her life:

PATRICIA: I don't know. You're sort of cute in a homely way. And it's always lonely when that civilian you're fucking calls out the name off your fake passport.

BARRIS: "All the information I have about myself is from forged documents."

PATRICIA: Nabokov.