How to design aluminum alloy melting furnace with nichrome coil heater of 800 watt 26 swg coil?
Sorry, but there is simply no way to answer your question. You have failed to provide the most important bit of information - how good is the insulation of your proposed furnace?

If it's a perfect insulator, even one watt of power will do the job (although it will take a long time to do it).

However, that is not a likely way to operate. 

Have you tried the Wikipedia article on Nichrome? I thought not. 

Let's take your starting point. 26 ga NiCr-A has a nominal resistance of 2.5 ohms per foot, so at room temperature your spool of wire will have a resistance of about 74 ohms. If you were foolish enough to apply 220 volts to it, and the resistance did not change, you'd get about 1800 watt. The resistance would change, though, and probably by a factor of 3 or 4. So figure on something like 500 watts.

Is this enough? As I say, there is no way of knowing. I suggest you get some blocks of firebrick and actually make an oven. Then wind a coil out of your wire, making sure you include a means of keeping the individual layers from touching, and get a thermocouple and thermometer on eBay, and then do some experimenting.