How does this blinking circuit with op-amp work?
No, since this circuit is a mess and underterministic.

Note the positive input driven only thru a capacitor to ground.  Unless this is some special opamp that biases the postive input in some known range (there are actually amps that do that, usually meant for audio applications), the voltage on the positive input is totally dependent on the sign of the leakage current and not a function of the signal.

What someone was possibly trying to do but seriously messed up, was to present the immediate attenuated output signal on the + input and a low pass filtered version of the output signal on the - input.  Such a setup can be made to oscillate with predictable parameters, but that's not how this circuit is wired.