How are flashing LED circuits made?

You could look up circuits that use the chip known as a "555 timer", but you need college level math and physics to begin to understand much electronics.

Basically you have a circuit called an oscillator which does the on-off-on part. The output of that controls a transistor which acts as a switch, turning on and off the current through the LED.

Google 555 flasher circuits for examples. The 555 is a common IC (chip) which can act as an oscillator.

Don't let anyone tell you you need college level maths and physics to understand basic electronics, you don't.