Circuit to produce chattering relay
If I undestand correctly, you want to use the relay coil to generate a high voltage by switching it very fast. 

Currently your circuit looks something like this:







simulate this circuit &ndash; Schematic created using CircuitLab

As you can see in the circuit, the coil of the relay is active and will switch the output. Because the inductor tries to keep a current flowing, but because there's only a very high impedance connected to the output (Out), you will get a very high (negative) voltage on that pin. 

Usually we don't want this effect and we put a reverse connected diode over the inductor of the relay (called flyback or kickback diode). 

The circuit will start to oscillate by itself, because the coil is not getting any current, it will fall back to the NC position and then reactivate. Therefore I don't see why you put an arduino to it. First of all an arduino cannot supply the ammount of current needed to operate the coil of a relay and secondly it does not need to switch, you just need a fixed voltage on the input. 

Lastly I would like to remind you that relays have a limited operating life, and when switching very fast it will not last very long.