our own subjectivity is necessarily dependent on our specific brains.
There certainly appears to be at least a correlation between brain states and conscious experiences.
But I'm not sure that rules out reincarnation completely.
Reincarnation isn't necessarily about the exact same self (which is an illusion in buddhism) or consciousness being born into another thing, but has more to do with a process of energy transference tied to the law of karma, as far as I know.
So it could go something like this: there is a process of conscious awareness/subjectivity from the point of view of a creature (c1). That subjectivity is certainly connected to the brain of the creature, but we don't know how exactly. Could be identical with brain states, could be an epiphenomenon, could be psychophysical parallelism. When the creature dies, the energy which made up that process of conscious awareness gets transferred (how? mystery) to a different creature (c2) at the point of its birth at some other point in time, and the process of conscious awareness begins again. (c2) doesn't remember 'being' (c1) because the specific neuronal structures which constituted the experiences and memories of (c1) no longer exist (just like with one and the same creature, it might completely forget about all its childhood experiences, but that doesn't mean that it didn't have those experiences, or that its current conscious experiences are not causally connected to the earlier childhood experiences).
I don't see a logical contradiction here.
I get what you were saying with your original point, i.e. if 'I' am the sum total of my brain states, then 'I' can't reincarnate, since any other being wouldn't have the exact same brain states (i.e. the neurons, chemicals, molecules, atoms would be different ones), so they wouldn't be 'me'.
But, neither could I be identical with the sum total of any particular set of brain states, since neurons, chemicals and molecules in the brain are constantly dying, regenerating, rearranging themselves etc.
The 'mind' can at most only be the product of ever-changing but causally connected structures and interrelations in the brain, the product of processes.
So, conscious experience/subjectivity can only be a process too, and there is no
a priori logical reason why it couldn't be connected, in ways relevant to reincarnation, to other conscious experiences/neuronal structures at other spacetime locations.
I probably haven't explained this very well and it might not even make much sense.
I do like this quote by Voltaire though:
"It is not more surprising to be born twice than once. Everything in nature is resurrection."