Borthwick suggests that the stream found its start in RSS:
Figuring out where the stream metaphor came from is hard — my sense is that it emerged out of RSS. RSS introduced us to the concept of the web data as a stream — RSS itself became part of the delivery infrastructure but the metaphor it introduced us to is becoming an important part of our everyday day lives.Admittedly, in the sense that RSS gave us realtime bits of information, we can view it as the (or at least "an") origin of the stream. But RSS developed along with tools that allowed us to determine, to control, what entered our streams. Rather than being inundated without ever really being asked what we want to have flowing to us, with RSS we were able to set up our readers to accept and reject what we did or didn't want. We were in charge. The stream never asks. It simply keeps feeding us nonstop.