I have no flat rate/free shipping methods

PS:

and this is what my “shipping options” tab looks like – no free shipping option to enable: https://i.imgsafe.org/4c298c6f90.png

Methods are added to zones – see https://docs.woocommerce.com/document/setting-up-shipping-zones/

This does not allow free pickup on a per-product level however. Local pickup is a method that apples to the cart as a whole.

Got it- thanks!

I there a way to have it only show for certain shipping classes?

You’ll need an extension like Conditional Shipping and Payments in order to do this: https://www.woothemes.com/products/woocommerce-conditional-shipping-and-payments/