I think it worth mentioning the dd method which will work with any Distro. I think all Distros and all Puppies are iso hybrid now and so this method should work. I just tried it it with Puppy Bionic64 in Ubuntu and it works fine. The slight worry is that if you get the instruction the wrong way around then it can wipe your hard drive. Anyhow, these instructions should work.
1. Download any Linux Distro of your choice including any Puppy.
2. In Ubuntu open terminal and navigate to where the downloaded iso is. Instructions "cd /home/user-name/Downloads" and "ls" to make sure iso is there.
3. Plug in USB stick and in Ubuntu it will automatically be mounted as sdb. Type "lsblk" to make sure this is the case as if you get the drive wrong you can damage your data.
4. Type "sudo dd if=name-of-puppy.iso of=/dev/sdb" and type password when requested
5. Wait for write process to complete which will be indicated by the terminal going back to awaiting an instruction.
6. Remove or Reboot and use your Puppy.
NB. The " " are not typed, they are just used to show the command within is what is needed. And to reduce typing you use the tab button which will automatically add the rest of the details. For instance if you had some slackos in the Download typing "sl" and then tab will give "slacko" and so typing "6" and tab will give slacko64-7.0.iso