I have worked with metal clay before for jewelry work. Metal clays are metal mixed with a binder. You work it just as you would a standard clay product. When it has dried you can fire it in a Kiln at a temperature around 1700 degrees (varies depending on the specific product used). The firing burns away the binder and sinters the metal to form a solid object. Typically the process results in shrinkage of around 10%. Again, this varies depending on the metal clay being used.

Metal Clays come in a variety of forms. I've used silver, copper, and bronze. Manufacturers are coming out with new varieties all the time. Firing silver clay typically doesn't require any special treatment. On the other hand copper and bronze clay typically have to be fired in activated charcoal to control the oxidation.

Some people do fire small clay pieces using a torch but it is a much more controlled process to use a kiln. For example, the copper clay that I currently have requires ramping your kiln to between 1700 and 1800 degrees and then to hold at that temperature for 3 hours.

There has been a lot of money invested and a lot of work done to create the metal clays that we have today. That being said there are now people who have built upon that knowledge and produce their own metal clays that they sell on the internet. So it isn't impossible that these folks could come up with a metal 3d printer filament that would operate the same as metal clays do. However, the binders that are used in today's metal clays aren't at all flexible and would not work well to create a filament. So, a new plastic based binder would have to be created that would burn away cleanly, would be flexible enough to wrap on a spool and feed into a printer, and could support enough metal in it to minimize shrinkage during the firing process. I believe this could prove to be quite challenging.