So the bike will only stop when the ignition switch is off. Lecy aint my strong point but it may be possible that the ignition relay when energised is staying latched in even when the kill switch is turned off.
The Kill switch shouldn't have anything to do with the Ignition Relay.
Normally it is wired so that one side of the kill switch is wired to +12v from the fuse box and then when in the ON position it puts that 12 volts feed onto the Coils and Ignition modules, so when its in the OFF position there is no voltage to the coils or ignition modules hence stopping the bike running.
If I switch the ignition on without starting the bike up I can hear the fuel pump turning on and off when I flick the kill switch on and off. But if I start the bike up the kill switch has no affect.