If you think about practical armor, the chain-mail idea by Faed is the way to go. I'm going to answer more literally.
Turning metal into wires that can be knitted has the following problems:
It's really hard to produce. Wires are drawn by basically forcing them through a hole that's just not wide enough, so the metal needs to stretch to pass through. This requires the resulting wire to have enough strength to actually pull the rest of itself through. Now try that with micrometer-thick wires. Good luck...
If you manage to get wires that match the thickness of typical textile fibers, you'll have the problem that they will be much more stiff. Thin wires have a knack of breaking, and, once broken, they have little trouble working their way into your skin. So you need to make your wires significantly thinner than typical textile fibers to give them enough flexibility.
You should absolutely not use iron for this. The huge surface that you get by making the individual wires so extremely thin will mean that the resulting fabric will basically rust immediately. You can expose iron to humid environments as long as the metal is beefy enough to make material loss due to rust a minor concern. That's true for railways, it's true for chain-mails, but it won't be true for micrometer-thin wires.
That said, the first issue is readily addressed: There are methods other than drawing that can produce extremely thin wires. Like embedding several wires into a rod made from a different metal, and then drawing that rod into a wire. Once you etch away the enclosing material, you may be left with some real thin wires. The details are tricky, though.
The second issue just means that you have to work much harder on the first issue than you would have liked.
However, the last point is the real problem: There are only very few metals that won't react with our normal environment. Those metals are gold and some even rarer metals like platinum. All other metals do react with the environment in one way or another, including stainless steel. You may be able to get stainless steel of such high quality that you can actually can get away with knitting armor from micrometer-thin wires, but it does require very advanced metallurgy. And once you have such advanced metallurgy, it will be hard to explain why you don't also have sufficiently advanced weapons that will render your armor useless.
I mean, there is a reason why you don't see soldiers wearing armor anymore: The armor needs to be so thick that you have to put in on wheels and add a strong motor to it to be any help on the battlefield...
Finally, stainless steel is generally not the best choice when it comes to flexibility. It's generally more brittle than less inert forms of steel. And easier breaking of the fibers means less protection that the armor provides.
However, if you overcome/hand-wave the problems above, I see no reason why an armor made from such a material shouldn't be protective: The flexibility of the individual fibers means that they will just bend and not break when a sword crashes into them. Provided the fibers are not just thin enough but also long enough, they will spread the force across a larger surface, and thus stop the sword from penetrating.
As a matter of fact, we do use such armor, we just don't make it from metal, we make it from Kevlar. Kevlar is nothing more or less than a textile fiber of immense tensile strength. Kevlar is superior to steel because
Other than that, a Kevlar vest is pretty much indistinguishable from your woven metal armor.