Flash chip cells are basically tiny electron traps, they consist of a tiny stored charge surrounded on all sides by an insulator. When writing to the cell you fill it with some electrons via (much handwaving here) a method of quantum tunneling. You can then read the cell by sensing the internal charge without disturbing it.

When not in use eventually enough charge tunnels out of the cell via random quantum tunneling events for it to read nothing. This is worsened when things are hotter, so maybe keeping your flash chips in the freezer would help.

Consumer flash memory, I probably wouldn't expect more than 20 or 30 years of offline storage out of it. The older chips would last longer, because their cells are bigger, and you're not trying to read multiple charge levels per cell like the newer stuff.

Added edit:

Magnetic media probably has a higher chance of surviving longer. Floppies from the 80s can still be read, for example, but they are low density media. You'd want something that separates the drive system from the actual magnetic media to stop bearing or motor failure from being an issue , so tape would be a good idea.

The problem is, of course, that you could end up with media you can't read as nobody makes the hardware for it. Tape drives have gone through a dozen revisions in the last 30 years as capacity has increased, but as long as you have the same physical tape cartridge you should be ok.

M-Disc is a blueray compatible media that doesn't use dye and should have a life of hundreds of years. But who will have a blueray reader on hand in the 24th century? I've got a USB M-Disc compatible writer for my backups, but in 30 years will I be able to pull it out of a drawer and plug it into a USB Gen 15 port and have it work with whatever software I have then?

I think we're going to have to do the manual duplication process for a while yet, until we finally settle on some universal petabyte storage crystals or something.