Bitcoiners have been thinking about this storage problem for a decade now. Secure electronic devices in faraday cages and tamper and water proof bags or engraved steel plates (possibly cut up and distributed) seem to be the way to go for storing small bits of extremely valuable information.
Or of course you can use multiple key storage techniques and have a 2 out of 3 or more type setup. It all depends on how valuable the information is.
Security against unauthorized use and data lifespan are separate concerns. They're not fully orthogonal—security tends to make things more brittle—but you can apply whatever form of security you like and then store the secured data in any way you like. Hardburn seems to have been talking purely about the useful life of the archived data. The charge in flash storage leaks, so the data is eventually lost if not refreshed. A flash drive is reliable for a year, but not a decade. If you want long term storage you're going to want something else. Paper would be fine for most uses. An ordinary printout subjected to ordinary handling is good for a few decades with reasonable storage conditions.
Or of course you can use multiple key storage techniques and have a 2 out of 3 or more type setup. It all depends on how valuable the information is.