How can I add a shipping method to packing slips?

You put it into your packing slip template wherever you want it. It’s just basic HTML in there essentially, so it’s entirely your choice as to where you want to display in within the page. I put it between the addresses and the items, but it’s really just wherever you want it.

Or if you mean where do you find the template, that was the answer to the previous question in this thread:
Settings > Shipping and delivery > Packing Slips > Edit template

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