While you can live boot ChromeOS Flex from the USB installer, Google recommends that you fully install it on devices. When you live-boot ChromeOS Flex, limited storage is available because of the layout of ChromeOS Flex's partition table.
ChromeOS Flex is a relatively large OS compared to common linux distributions. To make sure that you can use USB drives from as many manufacturers as possible to create your ChromeOS Flex installer, we reduce the size of the installer image, which limits storage space. For the moment, this is not a feature that can be changed.
To avoid keeping files on the limited live-boot USB drive, consider using a second USB drive, SD card, or Google Drive to store them.
Live booting is only recommended for temporary exploration or testing. We strongly recommend full installation for the best ChromeOS Flex experience.