It occurred to me that it would be a smart idea to put all my important travel info right onto a little flash drive stick. My question is whether it's safe to send a drive through the security imager or not?
I have done exactly that - no problem for me.
The various security scanners won't harm the drive or any other kind of memory stick. They are very robust.
My camera equipment including flash cards have been through security many times without an issue. You should be fine.
Since the flash drive carries digital rather than the old film, the security equipment doesn't degrade it. I've even sent a few through the washer and dryer accidentally and they were fine.