I see some thing he’s from the Allied forces due to his outfit.

In my headcannon, he’s the first Doctor to meet the MLP. He first met Rainbow and FLurtershy (when younger). And he’s met them time and again. And as an old man, he recruits them to help in a Silurian Ark. A Noah’s Ark only with dinosaurs, Ice Age giants, dodos, great auks, quaggas, blue antelopes, and many more extinct life. And replacing the flood with the Time War. And with Davros and a Dalek Fleet including a black Commander, black-dome Guards and Pilots, crimson dome Pilots, blue-dome Scientists, and Special Weapons Daleks. And he wears an olife-green scrim scarf, a cream Panama cap, a paisley-shirt, and an indigo waistcoat with amber tartan symbols which fit.
Also on my headcannnon, he’s the first to meet the ones from Tarzan, Brother Bear, Ice Age, and such. And when he’s in Tarzan’s world, he’s wearing a duster coat instead of the trenchcoat and a paisley scarf along with a Panama; fitting since it’s Edwardian times. And he helps them fight old Davros and his Daleks, and also uses a dao sword to fight the War Master’s katana on the Sahara Desert.

The War Doctor’s my top fave. Cranky but nice. Old yet tough; physically and mentally. Able to see through fibs. Gives people 2nd chances. More honourable than the 9th, and as self-sacrificing as the 5th. And a grand outfit; a Wild Western lawman fuse with a World War soldiers. Got me more into trenchcoats, waistcoats, scarves, fob watches, and bandoliers; and introduce me to Van Dyke beards and gaiters as well as to herringbone.