Crutchfield has a chart showing the recommended power wire size. Add up the amperage of all the fuses in your system and measure the length of the wire you will need. You'll find the recommended gauge on the chart. If you undersize your wire, your lights will dim when the bass hits (voltage drop).
I know others say it will be ok, but I don't recommend using the factory speaker wiring if you can help it. It will not be dangerous to use the factory wiring, but it will probably not sound the best. This is for the same reason as undersizing a power wire; voltage drop. I don't know the exact size of the wires in the BRZ yet, but in my WRX the wires were something like 22 gauge. They were extremely small. They will probably not be able to handle the demand on certain bass hits and will make the sound weak in the bottom end if you use the factory wiring. I would recommend 14 gauge for the speakers and possibly 12 gauge for the subs. If your lights dim then that's an indication that your wires are too small. It's better to oversize if you can.