Police are searching for the missing woman and her 10-year-old son, believed to be in Greater Manchester.
Kelly, 45, disappeared with the Knox on July 28.
He went missing from his home in Peachway, a town in South Gloucestershire.
But Avon and Somerset police investigators believe he may have traveled to Oldham and urged anyone who spotted him to call 999 immediately.
In a Twitter post, the force said: “Police and social services are concerned for the safety and well-being of Knox.”
Kelly is described as white, slender, about 5 feet 2 inches tall with brown hair and brown eyes.
If you see them, call 999 at 5221171972.