"I'll have to try and make one of those. Must it be of tool steel (or other high carbon steel), or can you make it work with mild steel as well?"
"No" to the last part of your question. Strikers won't work unless there's have a fair amount of carbon in the steel.
Some people make them out of old dump rake teeth or coil springs, including garage door springs.
I'd say that the lower the alloy (other than carbon), the better the striker will work.
My guess is that you need at least about 6/10th of one percent carbon to be effective.
For a "plain carbon steel" that would be 1060.
Coil or leaf springs might be made from 5160. You get the idea: the "60" means 0.6% carbon.
Personally, I use brand new W1 (1095, which has almost 1 percent carbon ---.95%--) steel that I buy in 3 foot sticks that are 3/16" X 1/4" rectangles from MSC. That way I know for sure what material I have and how to harden it.
By the way, it's not enough to make your striker from high carbon steel: You must harden the striker after you shape it if you want it to make sparks when struck properly against a flint.
This hardening process makes the striker VERY brittle. Some people draw (temper) the striker to a light straw to get rid of some of the brittleness so they are less likely to break if they fall onto a concrete floor.
It is also a good idea to normalize the striker after forging it, by heating it up to a medium red heat and then allowing it to sit at the edge of the fire, cooling SLOWLY for several minutes before hardening it. I'd say this is especialy true if you are using mystery steel.
I harden by taking the part to a couple of hundred degrees beyond non-magnetic and quench in water, but I quench only the working edge, so as to leave the "arms" softer so the striker is less likely to break if dropped. I don't temper mine at all. Make sure you swish that part around in the quench water or it won't harden well.
If you have any problems getting your newly-made strikers to make sparks, click on the "Decarb Issues---" link at the top of the page.
There are probably as many answers to your question as there are blacksmiths.