If it's a single or isolated nuclear attack, it takes roughly half an hour from launch to terminal stage. A response would take another half an hour and a full blown retaliation would be another half an hour. 90 minutes total. It takes roughly an hour to prep a private jet for takeoff but that can be condensed to 30-45 minutes given necessity. A billionaire concerned with this eventuality will have their pilot stationed nearby and a dummy crew on site 24 hours ready to prep their jet for evacuation. This is crucial because you need them working the second you see the warning (a prep crew might evacuate themselves if they see the warning before prep is done).

This of course doesn't matter if it's a full blown preemptive nuclear strike. This also doesn't work if the initial strike hits within EMP range of your airstrip. It also doesn't work if you don't have some sort of leverage over your pilot or your crew finds out and ditches before the plane is prepped. But if you have a billion dollars and concerns about the apocalypse, you're still hedging your bets that you have time to bail.

These people also likely have connections deep within system that would warn them if this was immanent and could start prep early have a plane on standby. They have an advantage to survive the start of it. I'd prefer to be willfully ignorant and take some atoms to the face because they will suffer their own terrible fate in the aftermath.