How can I Install Linux on flash disk with NTFS filesystem?

I think unetbootin does the job (installing ubuntu live cd on flash disk). You will probably have to install Grub on it too.

NTFS doesn't work very well with linux's file permission, you need a filesystem container (usually squashfs correct me if I'm wrong) that has a linux fs inside of your NTFS partition.

To install linux on a flash disk, I assume you want either How-To-Geek's Create a Bootable Linux Flash Drive or Create a Persistent One. From experience I know linux doesn't play very nice with NTFS, though it is possible. If memory serves, permissions on linux don't apply right on NTFS yet. Hope that helps!

Just download the iso, then, if you have a vm app, you can boot the iso. Otherwise just burn it to a cd or dvd, then boot to it. Click on try ubuntu, then click on dash home*. lookup start, then click on startup disk creater. Insert a flash drive to your computer, and give the flash drive control to the vm, if using one. Then hoose how much space you want to give to the flash drive for storing your files and settings. Or you can mae it so they will be deleted once you shut down. Then click create. Wait for it to finish. Once finished, shut down your computer/vm and once you boot up your flash drive, it will go to ubuntu. Then you can click try ubuntu again.

*This is for version 12.04 LTS Desktop.