Infestation by the Cheyletiella mite, which lives on the surface of the skin. It is called "walking dandruff" because the dandruff appears to move (these are the mites). It is a mild zoonosis.
This guide points you in the right direction and takes you to the vet; it does not diagnose.
Notice: this information is for general guidance and educational purposes only. It does NOT replace diagnosis or treatment by a registered veterinary surgeon. If you notice any symptoms, always consult a professional. Mizuu accepts no responsibility for the use of this information without veterinary supervision.