Perhaps you noticed that I put each { on it's own line. That makes it easier, to me, to see where a block of code starts and ends.
If you look at your code, you set blinking to true the first time the switch is pressed. The next time, you set it to false. Then true, then false.
However, you turn the LED on when blinking is true, but you do not turn it off when blinking is not true.