Enable copy/paste on html5 date field

By native?

No, a date input field behaves differently than a text input field.

Workaround

I had the same problem once and created a workaround.

When you dlbclick the input field, it temporarily changes itself to a text input field and automatically select its value. So you can copy the date by using CTRL + C

It also works when you want to copy a date from and text field into the date input field.

Register a focusout event to reset the input to its original state type="date".

// get all date input fields
let dateInputs = document.querySelectorAll('[type="date"]');

dateInputs.forEach(el => {
    // register double click event to change date input to text input and select the value
    el.addEventListener('dblclick', () => {
        el.type = "text";
        
        // After changing input type with JS .select() wont work as usual
        // Needs timeout fn() to make it work
        setTimeout(() => {
          el.select();
        })
    });
    
    // register the focusout event to reset the input back to a date input field
    el.addEventListener('focusout', () => {
        el.type = "date";
    });
});
input {
  display: block;
  width: 150px;
}
<label>Double click me</label>
<input type="date" value="2011-09-29" />
<input type="date" placeholder="paste the date here" />