Create a blinking LED circuit with a z-diode and a capacitor
No, your circuit will never work with the ordinary Zener diode and low supply voltage. You need a tunnel diode or NPN transistor or some other negative resistance two-terminal device. Because the negative resistance region is the key here.  

And this circuit will not work with all NPN transistor and will never work with PNP transistors.

To reduce the risk of failure builds a different circuit that uses a classic multivibrator. Because the original circuit is very fussy and for sure will not work with such a low supply voltage.