Tough call. Very tough call.
Fire fits his personality as well as the fact he is the anime counterpart of a character called Red. Plus his connection with Ho-Oh (surprised that wasn't brought up)
Flying connect him to all the different flying types he's had
Fighting is similar to fire in the sense it fits his personality
Grass would be neat since he's had nearly all starters. But only if that gives him a Chespin
Dragon is another one that fits him and his personality.
On a more lowkey option, ground is kind of viable for him if you think about. Donphan, Gliscor, Torterra, Gible (with potential to Garchomp) and Krookodile. Dual-typing allows some diversity here (even if Donphan is pure ground)
So I have no idea so my vote would be on him pulling a GSCgame!Blue and having a gym without a type speciality. Or maybe even pokémon of the types pointed above.
On another hand, if Ash was a Frontier Brain, I could see him being a specialist on attack and speed (basically sweepers)
EDIT: forget dragon-types for some reason. So there's another one for the list.