How to add flat rate in Drupal Commerce?
Check "Shipping methods" tab (or go to .../admin/commerce/config/shipping/methods). Flat rate should be listed here.

If not double check that flat rate module is enabled?

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When viewing page Store > Configuration > Shipping there is few tabs like "Shipping services" and "Shipping methods" but below them is another set of tabs, which should include "Flat rate" and should be chosen before Add a flat rate service link becomes visible on that page.