In order to change the style of the Stripe credit card form in Checkout, you will need to place the below sample code into the Checkout Style template:
input[type="text"].flat, input[type="password"].flat {
background: transparent;
width: 100%;
box-sizing: border-box;
-moz-box-sizing: border-box;
box-shadow: none;
color: #40526a;
outline: none;
border: 0;
box-shadow: none;
height: 40px;
padding: 10px 10px 10px 10px;
}
These are default styles. They can be updated and affect the inner input styles.