I did not know there was a special "draw" file.  I draw file with regular smooth cut Nicholson's run at the same angle the teeth are cut.

Boats

Web like you my Green Mt barrel was blued as it came from Green Mt.  Draw filing would have made a better finish though. As is was good enough,

Boats

Use a smooth single cut file and you will be fine. If you use a 50/50 mix of dark cutting oil and kerosene as a lubricant when filing you will most likely get a better finish. The lube will also help to reduce clogging up the file. You can also use chalk on the file, but personally I like the oil mix better. The lube also helps give a better finish with emory paper as well.

Jesse

The blue on GM barrel is from the heat in the stress relief oven.

One method,not mentioned here ,is to buy a brand new,not used lathe file.
I cut the tang end off where the teeth start out,and same with the other end,with an abrasive saw blade,and round off the cuts,with a belt sander.
The file is laid flat on the flat,and pushed towards one  end.
wear leather gloves,ans the small chips will end up in your fingers.
I use both hands,and guide the file with my fingers.
Trying to keep a file perfectly flat,when using a 10 in mill file can be hard,especially to newbies.
I use a dry waxy lube,called burr life. It will keep chips from filling up the file teeth.
You just rub it into the teeth,like you would chalk.
I keep a 5#block of lead handy,to smack the file on to clear chips. (No DO NOT use your lathe bed!)And keep an eye on the file,no matter what method you use,for chips stuck in the teeth. You will gall the flat of the barrel.
Clean them out immediately,with a file card,and pick.
A lathe file,has teeth @ app a 60 deg angle ,and shear off the chips.
This method,will not work on the breech end of barrels with a tulip next to the threads,you will have to hand finish that area sama as with a normal draw file.
I saw another builder,has an aluminum jig made to hold one inch wide roll abrasive.
He has nylon fences to guide it along the barrel,and the strip,is held with a home made clamp on both ends on top.
He was using a dark sulpher base oil with this.

LOL on the sweeping up of chips, although they will not get stuck in the wife's feet, since I don't got one of those they may end up in my feet and that wouldn't be a good thing.
Thank you all for your reply's, now to make a fixture to hold the barrel and order a file. 
I am not sure where my barrel was made in the run but it has very distinct marks that do need removed. I did have a thought of leaving  one flat unfinished as the current finish would make a very nice non glare surface but it might piss my smith off due to having to index up just that particular flat.  We will see when it get into it more. 
Sam

But can you get belts fine enough to finish or do you just take out the deep nicks and scratches with it and then work the rest by hand?  And how fine a grit should you use prior to bluing.  I recall reading that the best blue jobs aren't on mirror finish but over something called a '500 grit wire wheel', something I've never seen for sale.