If you're using the flash drive as a block storage device with a root partition, I think just about any distribution would fit your requirements. Just try experimenting with it and make sure that both your machines can boot into the flash drive.
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Linux is a family of open source Unix-like operating systems based on the Linux kernel, an operating system kernel first released on September 17, 1991 by Linus Torvalds. Linux is typically packaged in a Linux distribution (or distro for short).
Distributions include the Linux kernel and supporting system software and libraries, many of which are provided by the GNU Project. Many Linux distributions use the word "Linux" in their name, but the Free Software Foundation uses the name GNU/Linux to emphasize the importance of GNU software, causing some controversy.
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Ok, thanks. I just wasn't sure if there were compatibility or stability issues with certain distros from switching machines so much.