The easiest option requires two flash drives.
Load the contents of the ubuntu live iso onto flashdrive A, which is probably smaller than your 32Gb flashdrive B.
Plug flash drives A and B into the macbook
Boot onto flash drive A, run the install process
During the install, have it format flash drive B as the primary installation drive and make sure it writes the bootloader on there too
Enjoy your new linux flash drive B.