Hi,
This is a cute little circuit really. You dont see this kind of thing too often anymore. Where did you find this circuit?
At first glance it doesnt look like an LED flasher. It looks like an LED modulator, where the input light level modulates the output LED light level (like an fiber optic repeater might work). If there is very little ambient light level present the LED turns on which produces light, but if we apply some source of light to the light dependent resistor, the LED starts to dim maybe turn off altogether at some point. Now that would be the end of the analysis, but something else interesting comes into play. What if we shine the light from the LED onto the LDR? With the light from the LED shining on the LDR, suddenly the LDR resistance decreases, which turns the first transistor on a little harder which decreases the drive to the second transistor, which then dims the LED or even turns it off. The light from the LED now dimmed, causes the LDR resistance to increase again, which then turns the first transistor on a little less than before which means the second transistor turns on a little more, which in turn turns the LED on harder. Thus we have a feedback loop which given the right conditions, could cause an oscillation which of course will make the LED blink on and off repeatedly. Im guessing that the capacitor helps to set the oscillation frequency.
[ADDED LATER] I didnt recognize the basic circuit configuration at first as a rare type of oscillator circuit that can be made to oscillate without the light shining from the LED to the photo transistor.
Would be a bit interesting to analyze a little more. Would also be interesting to think about what could be placed between the LED and LDR to change the frequency when used in that mode.