It cannot be used to forge iron. If the kitchen is well ventilated, you could maybe do casting with some softer metals, but the temperatures needed to forge iron and steel are higher than your kitchen stove will provide, and if you heap coal on your kitchen stove and try to use it as a forge you will destroy it (among other risks like suffocation and burning your home down).
A forge really needs to be placed outdoors or in a well-ventilated workshop (with a non-flammable floor... dirt, stone, concrete), and should be made of brick or very thick metal. One cheap way to make a forge is to use a brake drum like a bowl... cut a hole in it to allow air in from the bottom, weld on a piece of pipe and install a flap in the pipe to control airflow. This generally requires a welding torch and some basic metalworking tools, of course.
You can fill this with coal, and with a good bellows it will get plenty hot enough for most blacksmithing tasks. Because heat rises, the drum will get less hot than the steel you're working with. An anvil can be any good solid chunk of steel, a chunk of old railroad track works well, or anything sufficiently solid with a flat surface to work on. Places that handle industrial scrap might sell you something suitable for cheap, just slightly more than they would get from sending it to be melted down.
If you can get a real anvil though, even if used and a bit battered, that's much better, the horn has many shaping applications and the square hole is great for quickly and easily creating right angle bends.
You do need real coal though, for most things. You can make do with charcoal for mild steel, but not for any tools that need to any real hardness.
It's also possible to make a gas forge with a blowtorch and enough bricks, but I don't really know the details, I've seen videos of them but never worked with one. It's terribly uneven heat though, a real gas forge will have multiple flames to spread the heat evenly.