If you're leaving the differential and (obviously) the seals inside, then you don't want to use anything like a bottle brush action that is going to push stuff inside. After all, "inside" is inside can far too easily become inside the differential itself.
Nope, best to do something similar to what JKH said (but not exactly in this case) and create a "scraper" that you can insert all the way without pushing anything further in, and then use it to pull all the junk outward only.
One of the members here posted theirs up just last week I think. They used all-thread too I think, but you can use anything from an old broom handle to a wooden dowel to all-thread or whatever you have on hand.
If you don't already have something the right shape and size, then cut a large washer in half, or maybe just lop off a third of it and attach it to the end of the handle.
From there you can insert it into the tube with the flat side down so as not to push anything inward, then spin it 180 and use the rounded end to pull junk out..
You want a pretty good size washer, but not so big that it's a tight fit into the tube. Just make it easier if you can maneuver it a bit when it's inside.
If you really want to flush it, you can still remove the cover and use some kind of liquid action in the tube. Then anything that does make it past the seal lip can be cleaned out of the bottom of the diff housing.
Just be careful as you can and not flush with power and blow gunk all over the insides.
I think I have that described in basic terms. Look for that other thread and see if the people that have actually done it a few times can add more details.
paul
