I was just wondering if it is possible, with just a digicam and a
USB flash drive (no computer, out in the field) and some sort of
connector, to download the pictures from the camera and store them
on the flash drive.
I don't know of any but it is a good question and lets take this one more step.
Why don't any of the cameras talk directly to USB mass storage devices? They have the file system support already.
Imagine buying any USB mass storage device, say 250GByte drive and storing to it. Yes, i know there are all kinds of devices around that let you download into them and view them but they are relatively small in storage and expensive in price. You already have a screen.
And yes, there is a difference between USB slaves and masters, but most digicams can talk to printers so they can control both ways.
USB 2.0 download to USB mass storage devices would be a big step in the right direction. It could just put the file into a DCIM subdirectory using FAT32 file system.
So for less than $200 you could get 180GBytes of mass storage that would have a small form factor and you would hardly ever run out of space on that vacation

. And yes, you could take a laptop but who wants the hassle?
some enterprising camera company could even market this thing themselves, say Canon or Olympus etc.
David