Mine is I think 8mm 'silver' anchor rope. I can say from experience this will fail before your kite lines will

Interesting point Lostdog makes, personally I'd prefer the tether weaker that the sum of the kite lines (or have a safety release included (or weaker
and with a release)).
If something goes wrong and the kite powers up and starts smashing around I'd rather the tether snap and have the kite fall fairly harmlessly from the sky than have the tether stronger than the lines and have the lines or kite start snapping and ripping apart, and flailing around until the kite and/or lines disintegrate. Both scenarios have a kite tumbling downwind eventually, one intact, the other with terminal damage.