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Remove a given Flat Rate when Free Shipping is available @ WooCommerce Cart / Checkout 
Clear Customer Sessions – WooCommerce System Status Tools
If Free Shipping is available, you possibly don’t want to show the other premium shipping options. WooCommerce shows by default all shipping rates that match a given shipping zone, so it’s not possible to achieve this from the settings alone.
Thankfully, the “woocommerce_package_rates” filter allows us to manipulate the shipping rates before they are returned to the frontend. In this example, we will disable all shipping methods but “Free Shipping” so that free shipping remains the only possible choice.
Here’s the code to add to your functions.php. Enjoy!
PHP Snippet #1: Unset Specific Shipping Rate When Free Shipping Rate is Available
To find the “shipping rate ID” e.g. “free_shipping:8“, please see the screenshot at the bottom of this other tutorial: https://businessbloomer.com/woocommerce-disable-free-shipping-if-cart-has-shipping-class/
/**
* @snippet Hide one shipping rate when Free Shipping is available
* @how-to Get tutoraspire.com FREE
* @author Tutor Aspire
* @compatible WooCommerce 6
* @donate $9 https://tutoraspire.com
*/
add_filter( 'woocommerce_package_rates', 'tutoraspire_unset_shipping_when_free_is_available_in_zone', 9999, 2 );
function tutoraspire_unset_shipping_when_free_is_available_in_zone( $rates, $package ) {
// Only unset rates if free_shipping is available
if ( isset( $rates['free_shipping:8'] ) ) {
unset( $rates['flat_rate:1'] );
}
return $rates;
}
PHP Snippet #2: Unset ALL Shipping Rates in ALL Zones when ANY Free Shipping Rate is Available
/**
* @snippet Hide ALL shipping rates in ALL zones when Free Shipping is available
* @how-to Get tutoraspire.com FREE
* @author Tutor Aspire
* @compatible WooCommerce 6
* @donate $9 https://tutoraspire.com
*/
add_filter( 'woocommerce_package_rates', 'tutoraspire_unset_shipping_when_free_is_available_all_zones', 9999, 2 );
function tutoraspire_unset_shipping_when_free_is_available_all_zones( $rates, $package ) {
$all_free_rates = array();
foreach ( $rates as $rate_id => $rate ) {
if ( 'free_shipping' === $rate->method_id ) {
$all_free_rates[ $rate_id ] = $rate;
break;
}
}
if ( empty( $all_free_rates )) {
return $rates;
} else {
return $all_free_rates;
}
}
Shipping rates not hiding after implementing these snippets?
You probably need to:
a) empty the Cart and start testing again
b) clear customer sessions: