How about this method that I have read on the internet which does not use a face plate but the flywheel must be small enough to be held fully within the jaws of the lathe chuck :
1. Hold flywheel ( 3.5 or 4 inch) in the lathe chuck by the outer rim ( They recommend a 4 jaw chuck but I am not sure why ?)
2. face the hub and the rim on one side.
3. Spot drill with 6mm spot drill bit
4. ream out to correct size. (I have been thinking of using 6mm axles instead of 1/4 inch)
5. take flywheel out of chuck and fit mandrel
5. place mandrel in lathe and face the other side
6. finish by facing the main outer surface of the flywheel
I have been looking at mandrels from Arceuro : straight shank expanding mandrels (5.5mm to 7mm)
**LINK**