Can a flash application (SWF) access the serial data on a USB port?
No. A web application cannot access user's machine without his permission. An SWF on your hard disk cannot read anything outside its folder.
Maybe :) Flash alone cannot handle that.
As far as I can think of you can either:
Use a socket server (written in java,c#, etc.) that will access the serial data and send it to flash. You could use a Binary Socket or an XML Socket, depending on how you write the socket server. WiiFlash uses a socket server and there are sources avaialable, might be a good start.
Make an AIR application and use the Native Process API to another application that will send the data.
It might a bit off, since there are a bit outdated, but have a look at flOSC and for some reason serial data/usb make me think of arduino, make checkout arduino2flash.
Can you explain what decive you're trying to get data from ?