GOAL = Remove flat rate when quantity is OVER 12

modification

add_filter('woocommerce_available_shipping_methods','remove_flat_over_twelve',10,1);
function remove_flat_over_twelve( $available_methods ) {
	global $woocommerce;
	$minimum_flat_rate_quantity = 12;
	if ( $woocommerce->cart->get_cart_contents_count() >= $minimum_flat_rate_quantity ) {
		// remove flat_rate shipping
		unset($available_methods['flat_rate']);
	}
	return $available_methods;
}

add_filter('woocommerce_package_rates','remove_flat_over_twelve',10,1);
function remove_flat_over_twelve( $available_methods ) {
    global $woocommerce;
    $minimum_flat_rate_quantity = 13;
    if ( $woocommerce->cart->get_cart_contents_count() >= $minimum_flat_rate_quantity ) {
        // remove flat_rate shipping
        unset($available_methods['flat_rate']);
    }
    return $available_methods;
}

/* from the other gist that seems to be so popular */
add_filter( 'woocommerce_package_rates', 'hide_shipping_when_free_is_available', 10, 2 );
function hide_shipping_when_free_is_available( $rates, $package ) {
    if ( isset( $rates['free_shipping'] ) ) {
        something about the quantity, then ---> unset( $rates['flat_rate'] );


    return $rates;
}

Run this and see if it's actually running when you expect it. Also check the keys. Remember that WooCommerce caches the requests by zip code, so change the codes when you're testing.

add_filter('woocommerce_package_rates','remove_flat_over_twelve',10,1);

function remove_flat_over_twelve( $rates ) 
{
    global $woocommerce;
error_log(__LINE__ . ' In woocommerce_package_rates filter');
    $minimum_flat_rate_quantity = 12;
    $num_contents = $woocommerce->cart->get_cart_contents_count(); 
error_log( __LINE__ . ' Cart num contents: ' . print_r($num_contents,1));   
    if ( $num_contents > $minimum_flat_rate_quantity ) 
    {
error_log(__LINE__ . ' rates keys: ' . print_r(array_keys($rates),1));      
        // remove flat_rate shipping
        unset($rates['flat_rate']);
    }
error_log(__LINE__ . ' Returning keys: ' . print_r(array_keys($rates),1));  
    return $rates;
}

Hi Brad I quickly ran the function on a mock instance to test and following works fine here http://test.pscreativeagency.co.uk/shop/. Once the basket has 13+ items the flat fee is removed. You do have to clear the WC Transients though as it did cache on me.

add_filter('woocommerce_package_rates','remove_flat_over_twelve',10,1);

function remove_flat_over_twelve( $rates ) 
{
    global $woocommerce;
    $minimum_flat_rate_quantity = 12;
    $num_contents = $woocommerce->cart->get_cart_contents_count();  
    if ( $num_contents > $minimum_flat_rate_quantity ) 
    {      
        // remove flat_rate shipping
        unset($rates['flat_rate']);
    }

    return $rates;
}