The "Running Spiral" first appeared on Greek seals from the Early Helladic II Period (c.2800-2300 BCE) and by 2nd Millennium BCE it had become a standard motif of Near Eastern art. It's not clear if it entered Egypt via direct contact with the Aegean or via Western Asia.
From el Armana.
New Kingdom, late Dynasty 18, reign of Akhenaten or Tutankaten, c. 1352 - 1329 BCE.