Using the custom styled Stripe button with Craft Commerce
Here is my working solution, basically all you need to do is grab the token from stripe and then submit it with the form.

&lt;script src="https://checkout.stripe.com/checkout.js"&gt;&lt;/script&gt;

&lt;form method="POST" id="payment-form"&gt;
  &lt;input type="hidden" name="action" value="commerce/payments/pay"&gt;
  &lt;input type="hidden" name="cancelUrl" value="/checkout/payment"&gt;
  &lt;input type="hidden" name="redirect" value="/orders/order?number={number}"&gt;
  &lt;input type="hidden" name="token" id="stripe-token" value=""&gt;
  {{ getCsrfInput() }}

  &lt;button id="paymentButton" class="button is-primary"&gt;
      &lt;span class="icon"&gt;
        &lt;i class="fa fa-check" aria-hidden="true"&gt;&lt;/i&gt;
      &lt;/span&gt;
      &lt;span&gt;
        Purchase
      &lt;/span&gt;
  &lt;/button&gt;

  &lt;script&gt;
    var handler = StripeCheckout.configure({
      key: '{{ cart.paymentMethod.settings.publishableKey ?? '' }}',
      image: '/assets/img/tfa-logo-128.png',
      locale: 'auto',
      token: function(token) {
        // You can access the token ID with `token.id`.
        var stripeToken = token.id;
        // Get the token ID to your server-side code for use.
        document.getElementById('stripe-token').value = stripeToken;
        document.getElementById('payment-form').submit();
      }
    });

    document.getElementById('paymentButton').addEventListener('click', function(evt) {
      // Open Checkout with further options:
      handler.open({
        name: '{{ siteName }}',
        email: '{{ cart.email }}',
        currency: '{{ cart.paymentCurrency }}',
        description: 'Membership',
        zipCode: true,
        amount: {{ cart.totalPrice|commerceCurrency(cart.paymentCurrency,convert=true,format=false) * 100 }}
      });
      evt.preventDefault();
    });

    // Close Checkout on page navigation:
    window.addEventListener('popstate', function() {
      handler.close();
    });
  &lt;/script&gt;
&lt;/form&gt;