You are best off writing a single file at a time.
You’ll likely find that your flash-drive’s bandwidth will get saturated pretty easily. (The source drive is unlikely to be the bottleneck.) While USB 2.0 can transfer upto 480MBs, your flash-drive is probably limited to ~20MBs. This means that when you transfer a couple of files from a hard drive(s), it will max out the flash-drive’s write speed, and each file will be written slower since they have to share.
Also, by writing multiple files at the same time, you increase fragmentation because unless the space for the files is fully allocated as soon as the transfer starts, they will end up being broken into chunks as the files are transferred.
(Fortunately because flash-drives are solid-state, there is no head that has to thrash back and forth like it would if you transfer multiple files to a hard-disk.)
Another drawback of writing multiple files at the same time is that the file-copy dialogs only indicate the progress and remaining time for that individual file, and it becomes next to impossible to estimate the total time because it is not linear (you cannot simply add them). Transferring them together will give you much more accurate feedback for the whole transfer.
If the source files are from different sources (do you mean different hard-drives? CD/DVD? network drive? or just folders?), then what you can do is to use a dedicated file-copying tool instead of Windows’ built-in function. Some options include the Microsoft TechNet tool Robocopy, which also has a GUI front-end, RichCopy (also from TecNet) which is an enhanced tool based on Robocopy, and Teracopy, which specializes in making the transfer as efficient as possible (and has a free version).