If you have that level of financial resources, then a natural gas-powered or propane-powered (liquefied, of course) plane is not infeasible. Survivalists favor those fuels because long-term storage is about managing the containers; the fuel itself will keep indefinitely.

In general however, most of these HNWIs' plans assume a resumption of status quo ante, or at the very least that they will find a spot on the planet where that happens. A Roman Empire-type civilization-wide collapse where knowledge outright disappears is extremely challenging to prepare against; at our tech level, you are essentially figuring out how to build much of a space habitat or generation ship. The population infrastructure to maintain the operational knowledge to sustain and produce at that tech level (not to speak of advancing it) is vast: tens of millions at a minimum.

If you prepare for that kind of end-of-civilization catastrophe with private resources, even billionaire resources, then you necessarily are building at a far lower tech level (a mix of 1800s and later periods' tech that can be recreated with more primitive tech, like transistor production), creating small villages and towns, and I have yet to hear of someone even doing that. Sid Meier's Civ series only barely nods at a hint of the vastness of the challenge to completely decouple indefinitely from civilization and keep going at a specific tech level: the skill tree to my knowledge hasn't been mapped out even for 1800s-level tech, such that a group of people with basic literacy can recreate the skill bases required.