Les,
The standard gearbox sprocket has 17 teeth - the 16 tooth you have is from either a 90+ or Competition Douglas. Unfortunately, because there is a shock absorber incorporated in the sprocket, it is not possible to go any smaller without the chain fouling the shock absorber boss. If your machine is one of the later type Dragonflies fitted with British Hub wheels (the ones with the pressed alloy covers on the brakeplates), it will have a bolt - on rear sprocket, which could be changed for one with more teeth. The only other modification needed will be to raise the back of the chainguard to give more clearance.
Regards,
Eddie.