You say that you told your young daughter it was a pirates finger that had turned to stone... Therein might be a clue to why it doesn't work..
Is it slightly conical and very round ? If so it could well be a fossil of a marine worm-like thing (can't remember their real name) rather than a decent piece of flint.
Another possibility is that it's been rolled around(bashed) in the tide for for so long that it's basically a lump of bits held together by little more than will-power, a good piece of flint shattered by the action of the sea.
You really need a nice sharp, solid, edge on a solid bit of flint big enough to hold on to whilst you strike it with the steel, or in your case with the file.
Don't use a toothed section of the file. Use the plain, un-toothed edge. The file teeth will only serve to break the flint. What you're really doing with this method is scraping a number of tiny flakes off the steel with the flint. Do it right and they're shaved off so fast that they get hot enough through friction that they burn. Yes... steel burns
The reason it works is because flint is so hard. Much harder than even the steel of a file. Hardness is allied to brittleness, hence the ability to shatter flint so easily.
If your file does not have an un-toothed edge, try grinding one edge smooth with an angle grinder, (Don't let it get too hot as this will ruin it) then try it with a good bit of flint.