JSFiddle - React, Tailwind, and code Playground

HTML

<div id="checkout-shipping-method-load">
  <select id="shipping-method">
    <option value="">SELECT</option>
    <option value="option1">1 twister ($14.99 + $6.99 S&H)</option>
    <option value="option2">1 twister ($14.99 + $6.99 S&H)</option>
  </select>
</div>

<input type="radio" class="radio" id="flatrate2" value="flatrate2_flatrate2" name="shipping_method">Flat 2
<input type="radio" class="radio" id="flatrate" value="flatrate_flatrate" name="shipping_method">Flat 1

JavaScript

$('#shipping-method').change(function() {
  if ($(this).val() === "option1") {
    $('#flatrate').prop('checked', true);
  } else if ($(this).val() === "option2") {
    $('#flatrate2').prop('checked', true);
  } else {
    $('#flatrate2').prop('checked', false);
    $('#flatrate').prop('checked', false);
  }
});