Does your scooter have a helmet lock, where you can lock in the strap? Probably in the form of a hook at the edge under the seat for example, so the D-ring is under lock and key but the helmet itself is hanging out.
As for jacket, I've seen people string a cable lock through the sleeve when locking up the rest of the bike, but it always looks to me like less trouble to just wear the thing.
Most of the newer scooters have underseat storage.
On that note I always leave my jacket and helmet sitting on the bike/scooter and have never had any trouble.