Can't able to detect Square wave from 74HC14
The only issue in your code is due to the delay in the pin control. You can solve it this way:

void loop()
{
    static int last_button_state = LOW;
    static unsigned int push_count;
    static unsigned long last_press_time;
    static bool kPinPressed = false;
    int button_state = digitalRead(button_pin);
    unsigned long now = millis();

    // Record when the button is pressed.
    if(last_button_state == LOW &amp;&amp; button_state == HIGH)
    {
        push_count++;
        last_press_time = now;

        digitalWrite(kPin, HIGH);
        kPinPressed = true;
    }

    if ((kPinPressed) &amp;&amp; ((now - last_press_time) &gt;= 20))
    {
        digitalWrite(kPin, LOW);
        kPinPressed = false;
    }

    ...
}


So you turn on the output, then after 20ms you turn it off.

There are just a couple of things not clear for me. What is the last picture? What are the yellow and pink traces? Why is it not behaving correctly? What are the readings on the serial interface?

And most important... What is the time scale? Is it really 10ms/div?