I had set up the Shipping Method incorrectly. I initially set up a new Shipping Zone which is why I wouldn’t show. I realized I just needed to set up a new Shipping Method within the Shipping Zone that has the Flat rate shipping method so they would show together.
I also tried this which worked
[costs_table prop="qty" table="1-4|2-7|5-9|10-13|15-16|21-19"]
It probably would have worked using the initial shortcode I was trying to use but because the Shipping Zone not being set up right it wasn’t showing up.