The USB drive is automounted as a device, not a file system. To see what device node was created just look at the dates of the device nodes. The most recently added nSX where n is the new device, and X is a bunch of nodes for different partitions etc. If you added disks before this might not work so quickly trying a few of the 1sX devices might be needed.

ls /dev/dsk/?s?

The USB drive probably came formatted as a FAT file system. The dosXXX commands can access a FAT file system directly with no need to mount it as a file system. So if 2nX was the set of device nodes created when you first inserted the USB drive commands like the following should work. If you have one disk then 1s1 is the where the flash drive is.

dosdir /dev/dsk/2s1

doscp /dev/dsk/2s1:BACKUP.ZIP BACKUP.ZIP

Myself I usually use zip and unzip to bundle up files for easy transfer and viewing on windows machines from/to the flash drive.