I did a more extensive fire test with an "expired" Egg, and I'm thinking it might be a mix. Pure silicone will not sustain a fire (once you get it started burning it will stop rapidly when removed from the flame), whereas my Egg sample would sustain a flame. It also showed some melting, though not as much as a known-TPE toy, and it was also harder to ignite than a TPE toy.
It also passed a test of several days with oil lube slathered on it and still was stretchy and un-melted.
Not sure what it's made of.