I conclude, after reading this a few times, that I don't really know what you are labeling with the phrases "stream of consciousness," "stream of subjectivity," and "subjective timeflow." I don't know whether you mean to refer to one, two, or three different things, nor how I would recognize that thing (or those things) if I found an instance of it (them) in my oatmeal, or how I could tell if I subsequently lost it (or them).

That said, if it's what I ordinarily understand people to mean by "stream of consciousness", which is roughly speaking a narrative, then I would agree that after duplication there exist more of those things than existed before duplication... for example, if copy X stubs its toe then its narrative includes some analog to "ow!" which copy Y's narrative doesn't include.

So, yes, I'd agree that there's a new stream of consciousness (or perhaps several, depending on how unified the mind being duplicated is) initiated in the newly created copy, though I would say that the corresponding narrative begins significantly earlier than that moment. (I am sympathetic to the claim that the narrative, instantiated in the copy, is fictional prior to that moment. That said, our narratives are sufficiently fictional in the normal case that I'm not sure it makes much difference.)

All of this seems entirely consistent with, for example, a timeless formulation of quantum physics.