The 15-year-old was reported missing from his Gloucestershire home on Sunday, May 2 at 8.30pm.
It is believed he travelled to Cumbria and then on to Scotland and is now in Edinburgh, possibly in the Leith area of the city.
A Police Scotland statement said: “Jack is thought to be travelling on public transport and on foot.
“He is described as being of a pale white complexion, 5ft 8ins tall, with short red hair, and of a slim build.
“When last seen Jack was wearing a black woolly beanie hat with a white motif on the front, black body warmer, grey top, and dark tracksuit bottoms.”
Police are appealing for anyone who has seen him or knows of his whereabouts to call Gloucestershire Constabulary on 101 and quote incident 396 of May 2.