Designing a 555 led blinker
Compare your circuit to this one:



This circuit has two LEDs, only one will be on at the same time.

You can remove one of the LEDs (and then also remove the resistor in series with it) and you'll have the most standard 555 LED blinker circuit possible.

Note how pins 4 (not Reset) and 8 (VCC) of the 555 connect to the + terminal of the battery. The fact that your circuit does not have this is a serious issue.

Your circuit is quite "unconventional". When starting out with circuits, just copy existing (and working) circuits. There are simply too many things you will miss (and get wrong) if you try and figure it out on your own. Later when you get more experienced (that might take years) you will be able to design circuits "from scratch". So just copy what works, it is the quickest way to learn.

Maybe the "designer" of the circuit you found got lucky and the circuit works for him. However it is then very likely that it needs the LEDs to be of a certain type. If yours are different the circuit might stop working.

My guess is that your circuit only works when using "power" LEDs like 1 or 2 Watt. If you use small LEDs rated for 20 mA then they will not light up. The circuit in my answer works with both types although the series resistor and supply voltage need different values for the "power" LEDs.