I don't use Puppy, but here's the brute force way:
Download the Flash *.tar.gz from Adobe
and decompress the tarball. As root, copy libflashplayer.so to the appropriate plugins directory. For Firefox, that's /usr/lib/mozilla/plugins; I don't know about Chrome.
If that directory is present on your system, it may well work for Chrome also. In my experience, several browsers search that target when looking for plugins because it's present on so may systems.
The tarball contains lots of other stuff, but I've never had to mess with that.