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Stephen Marshall's book Flies: The Natural History and Diversity of Diptera has an illustrated worldwide key to families.

Once you know you have a calyptrate fly in Oestroidea or Muscoidea, look at the course of the distal part of vein M. If it runs straight to wing margin you almost certainly have superfamily Muscoidea. The flies with a sharp right-angled bend in the distal part of vein M are Sarcophagidae or Tachinidae. In between you could have Muscidae or Oestroidea, but not Fanniidae.