functions.php

<?php
/**
 * Iconic WDS - disable Fee for local pickup.
 *
 * @return void
 */
function iconic_wds_disable_fees_for_flatrate() {
	$shipping_methods = WC()->session->get( 'chosen_shipping_methods' );

	$post_data = filter_input( INPUT_POST, 'post_data' );
	$data      = array();

	parse_str( $post_data, $data );

	if ( empty( $data['shipping_method'] ) ) {
		return;
	}

	$shipping_methods = $data['shipping_method'];

	if ( empty( $shipping_methods ) || ! is_array( $shipping_methods ) ) {
		return;
	}

	// Disable fees for other shipping methods except flat_rate.
	if ( false === strpos( $shipping_methods[0], 'flat_rate' ) ) {
		WC()->session->__unset( 'jckwds_same_day_fee' );
	}

}
add_action( 'woocommerce_cart_calculate_fees', 'iconic_wds_disable_fees_for_flatrate', 9 );