Does silicone rubber conduct electricity?

Does not conduct

silicone rubber

An insulator, and it retains that property at temperatures where most polymers have failed.

How it compares

Percentage of the International Annealed Copper Standard. Silver is the only element above 100.
Material	Conducts?	% of copper
silver	Conducts electricity	105%
copper	Conducts electricity	100%
gold	Conducts electricity	70%
aluminum	Conducts electricity	61%
aluminum 6061	Conducts electricity	43%
magnesium	Conducts electricity	39%
aluminum 7075	Conducts electricity	33%
tungsten	Conducts electricity	31%
brass	Conducts electricity	28%
zinc	Conducts electricity	27%
nickel	Conducts electricity	24%
iron	Conducts electricity	17%
platinum	Conducts electricity	16%
tin	Conducts electricity	15%
bronze	Conducts electricity	15%
chromium	Conducts electricity	13%
wrought iron	Conducts electricity	12%
tin-lead solder (60/40)	Conducts electricity	12%
lead-free solder (SAC305)	Conducts electricity	11%
mild steel	Conducts electricity	10%
pewter	Conducts electricity	10%
high-carbon steel	Conducts electricity	9%
lead	Conducts electricity	8%
tool steel	Conducts electricity	7%
tungsten carbide	Conducts electricity	5%
gray cast iron	Conducts electricity	4%
ductile iron	Conducts electricity	4%
Monel 400	Conducts electricity	3.5%
titanium	Conducts electricity	3%
stainless steel 304	Conducts electricity	2.5%
stainless steel 316	Conducts electricity	2.3%
mercury	Conducts electricity	2%
Inconel 718	Conducts electricity	1.4%
Ti-6Al-4V titanium alloy	Conducts electricity	1%
unidirectional carbon fibre composite	Conducts electricity	1%
graphite	Conducts electricity	0.1%

Diamond is an electrical insulator and simultaneously the best thermal conductor known — about five times better than copper at moving heat. Structure decides both, not composition.
Graphite is the same element as diamond and conducts electricity well, because its layered structure leaves one electron per atom free to move.
Carbon fibre conducts. People treat composites as plastic, and lightning strike protection on composite aircraft is a serious design problem because of it.
Pure water is an insulator. Tap water conducts because of dissolved ions — the hazard is what is in the water, not the water.
Air is an excellent insulator until roughly 3 kV per millimetre, at which point it ionises and conducts. That is what a spark is.

Does silicone rubber conduct electricity?: Does not conduct. An insulator, and it retains that property at temperatures where most polymers have failed.