It looks as if you found a good source for tow... That's great!
However, there are several other sources online, including Jas. Townsend, Smiling Fox, Turkeyfoot Trading, and Dixie.
Tow is certainly authentic for tinder, and there was a nice article in the Museum of the Fur Trade Quarterly a few years ago about an intact colonial era strike-a-light kit that had some tow included. I'll try to look up the issue to give the exact reference if you're interested.
One point about commercial flax tow that is not widely known or acknowledged is that a lot of it is treated with fire retardant. I'm serious. You'll want to check with your vendor, who may or may not know if it was treated. Your best bet may be to buy it directly from someone who grows and processes it themselves. I have bought tow from several sources, and I'm convinced some of it was treated. You couldn't light it with a match... it would just smolder, and never really catch fire. Some of it worked as it was supposed to, but none of it worked as well as jute fiber or the natural materials described below.
While natural (untreated) tow works as tinder, I have found there are other things that work better. I live in Florida, and locally I can scrounge dead Spanish moss (the black, fibrous material... It won't burn when it's in the fuzzy, gray-green state), palmetto fiber, and shredded inner bark of the southern red cedar, Juniperus silicicola. These are all free for the gathering, and for me they all work better than tow. I don't know where you live, but chances are you can source some natural material in your area if you are able to get off the pavement. Ruxton and Winthrop both mentioned using dry grass for this purpose out in the far west, although the grass here in Florida never really gets dry enough for good tinder.
I found a reenactor website from Texas a while back, and the author of the firemaking section said he cruises the local laundromats looking for dryer lint for his fire kit. Dryer lint?! We can do better than that!
If you are in a situation that prevents gathering natural tinder, I would suggest jute twine. I have used the natural jute from both Lowes and Home Depot with great results. It really makes first-class tinder. Cut a two foot piece, then cut that into quarters and pull it apart into fibers. Fluff the fibers and you'll have a "bird's nest" of just the right size, and it catches fire very easily. It works way better than flax tow, for me. You can carry a coil of the twine in your hunting pouch and use it as cordage for the odd tying or binding jobs you encounter in the outdoors as well as use it for tinder. I don't know when jute was first brought to the Americas, so can't vouch for its authenticity, but in this case that detail is not important to me.
Good luck with your firemaking. Just don't burn yourself!
Notchy Bob