Arduino- use millis() to do two (or more) things at the same time

The code is as follows

#define ledPin 13 // LED connected to digital pin 13
#define buttonPin 4 // button on pin 4
int value = LOW; // previous value of the LED
int buttonState; // variable to store button state
int lastButtonState; // variable to store last button state
int blinking; // condition for blinking - timer is timing
long interval = 100; // blink interval - change to suit
long previousMillis = 0; // variable to store last time LED was updated
long startTime ; // start time for stop watch
long elapsedTime ; // elapsed time for stop watch
int fractional; // variable used to store fractional part of time
void setup()
{
    
 Serial.begin(9600);
 pinMode(ledPin, OUTPUT); // sets the digital pin as output
 pinMode(buttonPin, INPUT); // not really necessary, pins default to INPUT anyway
 digitalWrite(buttonPin, HIGH); // turn on pullup resistors. Wire button so that press shorts pin to 
ground.
}
void loop()
{
    
 // check for button press
 buttonState = digitalRead(buttonPin); // read the button state and store
 if (buttonState == LOW && lastButtonState == HIGH && blinking == false){
     // check for a high to 
low transition
 // if true then found a new button press while clock is not running - start the clock
 startTime = millis(); // store the start time
 blinking = true; // turn on blinking while timing
 delay(5); // short delay to debounce switch
 lastButtonState = buttonState; // store buttonState in lastButtonState, to 
compare next time
 }
 else if (buttonState == LOW && lastButtonState == HIGH && blinking == true){
     // check for a high to
low transition
 // if true then found a new button press while clock is running - stop the clock and report
 elapsedTime = millis() - startTime; // store elapsed time
 blinking = false; // turn off blinking, all done timing
 lastButtonState = buttonState; // store buttonState in lastButtonState, to 
compare next time
 // routine to report elapsed time - this breaks when delays are in single or double digits. Fix 
this as a coding exercise.
 Serial.print( (int)(elapsedTime / 1000L) ); // divide by 1000 to convert to seconds - then
cast to an int to print
 Serial.print("."); // print decimal point
 fractional = (int)(elapsedTime % 1000L); // use modulo operator to get fractional part 
of time
 Serial.println(fractional); // print fractional part of time
 }
 else{
    
 lastButtonState = buttonState; // store buttonState in lastButtonState, to 
compare next time
 }
 // blink routine - blink the LED while timing
 // check to see if it's time to blink the LED; that is, is the difference
 // between the current time and last time we blinked the LED bigger than
 // the interval at which we want to blink the LED.
 if ( (millis() - previousMillis > interval) ) {
    
 if (blinking == true){
    
 previousMillis = millis(); // remember the last time we blinked the LED
 // if the LED is off turn it on and vice-versa.
 if (value == LOW)
 value = HIGH;
 else
 value = LOW;
 digitalWrite(ledPin, value);
 }
 else{
    
 digitalWrite(ledPin, LOW); // turn off LED when not blinking
 }
 }
}