The coupon is not valid for the currently selected shipping method.

Please paste a screenshot of the coupon’s Checkout tab.

Hello,
Please check it here: https://prnt.sc/vvn1ci

The coupon is configured for ‘local pickup’, the cart displays ‘flat rate’.

The requirement is to enable local pick only when coupon code is applied otherwise flat rate is set.

That’s not how it works.

You can create a ‘Free Shipping’-method and configure it so that it requires a coupon. You can set the description of the shipping method to ‘local pickup’. In the coupon’s edit-page tick the ‘Free shipping’-option. In that case Local Pickup will become available when the coupon is applied. See https://docs.woocommerce.com/document/free-shipping/ for more details.

Okay. Thank you.