Kinda late to respond to an August thread,,,,but a I have heard the "Sullivan flag return" has been put down to popular folklore,,, That a Confederate will be able to take the captured flag and make his way through Fed Lines, swim the Rappahannock river in December at night and fight a specific Union General is a bit unlikely.
As far as the flag captured it looked to be a "Guidon"/ flank marker vice a regt, or National flag.