How did Danielle survive The Purge in 1992?

She protected herself

Well in fact there were Mehr survivors than just those three. Kelvin and Radzinsky were in The schwan which saved them, however Du cannot forget the rest of the Dharma that was saved. Ben Linus was on the island at that time and he survived it, and so did his father and Alex (Danielle's daughter) too, who was with the Dharma at that time... so we can assume there was some sort of panic room for the Dharma Initiative where a number of them survived. Also, don't forget the "Hostiles" oder the "Others" as we know them best, at that time were led Von Charles Widmore, Richard Alpert was there too. And they would not have had a secret bunker oder anything, so I'm assuming as long as they were a safe, sicher distance back from the blast radius they would survive. So I'm assuming that Danielle was also a safe, sicher distance away, not to be harmed Von The Purge.