Draw filing is done with a normal file, or if you really want to get fancy, a Lathe file.
The lathe file has a slightly different angle to the teeth on it.
Having draw filed many octagon barrels, I can tell you that a standard mill ******* file (if well chalked to keep from loading up) works fine. Or, a double cut fine tooth file. The key thing is to hold the file at about a 20 to 30 degree angle and slide it sideways as it's drawn along the barrel. That way the cut is a "shearing" cut, and the file doesn't load up as easily and drag a filing down the barrel, scratching it. Every couple of cuts, tap the file off on the workbench to dislodge filings. Card if you see filings loading up the grooves at all. Nothing is more disheartening than to almost get it done, and drag a filing down the flat and have to file 10 more minutes to remove the scratch.
After getting the basic profile filed, the real work begins. Use a piece of 80 grit aluminum oxide or silicon carbide paper wrapped on a hardwood board about 2 inches wide. Draw file with it until all marks from the file are gone. Then, move on to 100 grit, 120, 150, 180, 220, 320, 400. Rotate the paper to get fresh grit whenever the paper starts cutting slow. You can work yourself to death rubbing a barrel with dull sandpaper that isn't cutting.
It's extremely important to sand more than you think it needs with the 80 and 100 grit. Otherwise, you'll get a couple of grits down the road and find you still have a few file drag marks that were hiding, and you have to go back to the 80 grit and re-do to get rid of them. Or, sand forever with the finer grits, to do the work of the coarser grits.
