Yes, a short section of an OLD file will make a very good flint striker. But you have to be careful when picking out your file. Many modern ones are made from low-carbon steel that has had the teeth case-hardened. So once you get past the teeth, there is not enough carbon in the remaining steel to work well as a flint strikers. Most old files will work. One modern maker that still makes a good all high-carbon tool steel file is Nicholson.
Here's my little write-up about making your own flint striker from a file without any heating or forging. It's pretty similar to what Mr. Fenna has already posted. Some of the old Boy Scout troops used to teach this as a Scout project.
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A good, quick, striker project that you can make yourself is to make one from a scrap of a file - without any heat-treating or forging. Clamp about 3 inches of a worn file in a vise, and hit it with a hammer on the flat side right next to the vise. The part sticking out should snap right off. Drape a rag over it first to control any "shrapnel". Now take that chunk of file and grind the teeth off of one of the narrow edges. Cool it often. If it's getting too hot to hold in your fingers, cool it right away in water. You need to grind off all of the teeth, and get down to solid metal. Also grind a bit of the teeth off of each side along that narrow side. Those teeth interfere with using it as a striker. Now grind off any sharp edges from breaking off your chunk of file - this saves on cut fingers. You now have a pretty good using striker. They work great. This is an old project that a bunch of the Boy Scouts used to do. They ain't pretty, and you have to use a "pinch" grip, but they make a great striker. And they are historically correct. In most archeological digs, when they find a small section of a file, the usually just view it as a broken file. A check of the wear on the narrow edges would quickly show if it was used as a striker. A bunch were.
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Hope this helps. Yes, I do have a number of strikers made this way from old files. There's one in the pickup truck, the car, one muzzleloader hunting pouch, etc. There's even one right here on my desk to "play" with - along with a Scottish Snail style, a Viking double Snakes style, a British Crown style, a Dutch double Snail style, and a Russina Fur Trade style. And these are just the ones lying about to "play with".
Oh, the ... toys ... we play with.
Mikey - that grumpy ol' German blacksmith out in the Hinterlands