I am looking for silicone sheet thin enough to breathe through - does such a material exist ?
I know that silicone is permeable to gas but am not sure a thin sheet would be permeable enough for human respiration at e.g. 10cm^2 area.
No, it's not possible.
Reason: At normal temperature, silicon(Si) has low density but when it gets oxidized(SiO2) it becomes denser. As it becoming denser it loses its permeability. That's why its not possible to pass air through it.