I see that Stripe can be used with CiviCRM but is Stripe Checkout ( https://stripe.com/checkout) an option with CiviCRM?
Stripe Checkout is not implemented at this time, but I would love to add it in the future.
Source: I am the maintainer of CiviCRM Stripe integration.
You can not use the checkout option for stripe if you are using it with CiviCRM.
As far as I'm concerned, you can use only direct payment option in stripe while making payment in CiviCRM.
Please refer a function doTransferCheckout() from link: https://github.com/drastik/com.drastikbydesign.stripe/blob/4.6-dev/CRM/Core/Payment/Stripe.php#L665
it says, 'Use direct billing instead of Transfer method.'