2 untested examples

void loop()
{
    int blink = 0 /* if you initialize incomingByte somewhere else, you should probably move this one there too */

    while (1) /* loop forever */
    {
        if (Serial.available()) /* read and process commands on the serial line */
        {
            incomingByte = Serial.read();

            switch (incomingByte)
            {
                case '1' : /* enable blinking */
                {
                    blink = 1;
                    break;
                }
                case '2' : /* disable blinking */
                {
                    blink = 0;
                    break;
                }
            }
        }

        if (blink) /* when enabled, blink leds */
        {
            digitalWrite(led2, HIGH);
            delay(300);
            digitalWrite(led2, LOW);
            digitalWrite(led1, HIGH);
            delay(300)
            digitalWrite(led1, LOW);
        }
    }
}

less expandable option but possibly working:

void loop()
{
    if (Serial.available()) /* read command on the serial line */
    {
        incomingByte = Serial.read();
    }

    /* if there is nothing on the serial line, then the previous value is used, so if you pressed 1 then it is
       still 1, anything else than a 1 will disable the show until you press 1 again */

    if (incomingByte == '1') /* when enabled, blink leds */
    {
        digitalWrite(led2, HIGH);
        delay(300);
        digitalWrite(led2, LOW);
        digitalWrite(led1, HIGH);
        delay(300)
        digitalWrite(led1, LOW);
    }
}