Hi,

You can just change the oil with a fresh one and change it again within another month or so.

Diff flush is not commonly done. My guess is that there's no need for such move as there's no combustion gas in those units. Only shavings of minute metal particles in case of normal wear. And these particles settle on the bottom within the centre housing.

If you're up to it you can open the diff cover (remove all the small bolts) and use spray cleaner to directly clean the gears inside. And remove any settled particles at the bottom. But I don't think that is needed here.

When my diff oil became black thick honey-like last time, I just changed the oil and repeated it within a few months again and again (4 times I think) till the oil became just like its original colour.

Make sure the diff breathing tube (a hard plastic tubing connected to one of the diff long arms) is not blocked.

Amarin.