WooCommerce REST API – GET Custom Checkout Page Fields for Order

Solution:

You can use the WooCommerce REST API v2 or later to get the Order Meta Data which includes these custom fields. If you GET an Order:

wp-json/wc/v3/orders/3454

it will include a meta_data array with these custom field values:

"meta_data" : 
[
    {
        "id" : 4672,
        "key" : "_shipping_method",
        "value" : [ "flat_rate:1" ]
    },
    {
        "id" : 4673,
        "key" : "_shipping_phone",
        "value" : "08 9632 7412"
    }
]