Can you run this linix from a flash drive if you have XP installed?
Sure. It's a bit of extra work to do, but lots of folks have set that up.
Trying it from a CD/DVD is even easier. If you download and burn the Linux Mint 13 DVD, for example, you can then boot from that disc and run Linux directly off of it, without actually installing it to your hard drive. Some distributions will even let you put Linux on your Windows desktop almost like an app you run. You don't have to toss Windows out to try Linux.
I think everyone should at least try it out.