As a proof of concept, I decided to try making a foil capacitor with a rubber dielectric. The plates were rolled together and secured with rubber bands to keep everything snug.

Specifications

Width: 15mm

Height: 15mm

Dielectric: Neoprene Rubber

Dielectric Thickness: 1.5875mm

Conductor: Aluminum foil

Leads: Aluminum foil tabs

Capacitance, 2.10nf (2,100pf)

Breakdown Voltage: ~25kv

Capacitance was read by connecting leads to aluminum tabs extruding from opposite ends of the capacitor. A Fluke 17B+ was used for measurements.

Wikipedia lists the dielectric strength of neoprene rubber between 15.7 - 26.7 MV/m which gives us a minimum breakdown voltage of around 24,923 volts and a maximum of 42,386 volts.