As long as you wipe and format the flash drive from the secure computer every time you use it, there shouldn't be any risk. I don't think even Stuxnet could have infected a linux machine that didn't mount or autorun the partition.
http://www.youtube.com/watch?v=D8Im0_KUEf8
Writing a Thumbdrive from Scratch: Prototyping Active Disk Anti-Forensics