There are several ways to get all WooCommerce Orders for a Customer.
Here you can get all Woocommerce orders for a customer by customer email id.
Use the following code to fecth WooCommerce orders for a customer.
The following code will fecth all orders for a current user.

$customer_orders = get_posts( array(    
    'meta_key'    => '_customer_user',
    'meta_value'  => get_current_user_id(),
    'post_type'   => 'shop_order',
    'post_status' => array_keys( wc_get_order_statuses() ),
    'numberposts' => -1
) );

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