In Woocommerce -> Settings -> Shipping, set up a Shipping Zone for Standard Shipping.

Add Shipping methods, in this case three: Standard Shipping ($7), Discounted Shipping ($5), and Free Shipping ($0).

Add the PHP to functions.php. To find out the id # of the rates, inspect the shipping methods in your browser;
the data-id of the table row for each is what has to go into the 'flat_rate:x' string.