As a check, are you burning the .iso on a CD first or trying to install it directly on a USB flash drive? The .iso is made for a CD. You would then boot Puppy from the CD and use the Puppy utility to create a bootable flash drive. (The menu path is something like Start --> Setup --> Install Puppy USB drive. I do not have a copy with me to check, but you should get the idea.) Once installed using the utility, the USB drive should work as you expect.
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