The kits will generally ship with a little extra wire, just in case. (When I pull wire, I will pull an extra 3" or so to be sure nobody gets short changed)
The amplifier uses a 1.5A slow blow fuse in the IEC/fuse module, which gives us a good idea of what the maximum instantaneous current might be (which is brief and during startup).
On the page below, there is a table that rates wire based on current and application:
http://www.powerstream.com/Wire_Size.htmAs you can see, for chassis wiring, 24 AWG wire is OK to provide 3.5A of current, which is more than enough for an idling Stereomour. When you look at the Power Transmission column, you'll see that 16 AWG is approximately rated for the same current, and this is the size of the power cord we ship with the kit.
If you wanted to twist up some green wire to be traditional with the filaments/heaters, the 300V rating will be sufficient and 22 AWG or thicker should work well.
(I'd always suggest building the kit with the parts supplied first, then making any changes thereafter)