So are you trying to display the time the button was clicked, and display it to the sender / recipient in their local time?

If so, you should just be able to use the Date constructor like so:

const date = new Date();

That will give you the UTC time. To convert to local time, you can use the .toLocaleTimeString() method. This would log your local time in US format:

const date = new Date();
console.log(date.toLocaleTimeString('en-US'));

So what you could do is have an event listener on the button, and when the button is clicked, create a new date, and convert to local time.

const button = document.querySelector('button');
const par = document.querySelector('p')

button.addEventListener('click', () => {
    const date = new Date();
  const local = date.toLocaleTimeString('en-US');
  par.innerHTML = local
})

<button>
Click me
</button>

<p>
</p>

JSFiddle: https://jsfiddle.net/f198wvdt/2/

Is this along the lines of what you're looking for?