I use Millers TRX Fully Synthetic oil in my Skoda Estelle trials car transaxle. (It dont arf stick to the components and casing!!!) The diffs have a tendency to wear out in time, knocking bits of the sun and planet wheels. I am fitting another diff but want to flush the existing oil residue out and as it is in pieces on the bench I cannot run it in the car with any kind of flushing stuff in it. What can I use to flush out synthetic oils?

Any hydro-carbon solvent will do (Kerosene, Paint Thinners) but you want to be careful not to wash oil out the gear clusters.

It might be an idea to fix a magnet the bottom of the gearbox to catch swarf,
Any time I have an engine or gearbox in pieces I been modifying the drain plugs to take a very strong magnet and also doing the same with power steering reservoir dip sticks --- it is amazing how iron and steel is getting pumped around in power steering fluid.