One thing you could do if you run Vista or Windows 7 is to use symbolic links. It's fairly easy (depending on your comfort level with command prompts and such) to set this up but you'd need to do it on each computer on which you ran the client.
Assume your flash drive letter is F and your Windows login name is Josh.
First, create a folder F:\SecondLife.
Then, *move* the folder C:\Users\Josh\AppData\Roaming\SecondLife to F:\SecondLife and rename it "Data".
Then, *move* the folder C:\Program Files\SecondLife and rename it "Bin".
Next, open a command prompt as an administrator (cmd.exe, PowerShell will not work for this) and type:
MKLINK /D "C:\Users\Josh\AppData\Roaming\SecondLife" "F:\SecondLife\Data"
MKLINK /D "C:\Program Files\SecondLife" "F:\SecondLife\Bin"
Now, Second Life can go on happily writing files to the locations it thinks it installed to, but really it is redirected to the flash drive.