Radiator flushing

Other than removing it.

A turkey baster works well to suck out the contents,

To maybe get in there a little deeper, a add a short section of clear vinyl hose to the basters tip.

Another route might be to set your "shop vacuum" up to suck liquids (usually remove the vacuum's filter)

Insert a small tube (such as 3/8 fuel line) into the vacuum's larger hose and duct tape the two together making a good seal.

Now you sort of have a shop vacuum with a mini hose, use it to suction out the contents of the reservoir.

I have a picture similar of the shop vacuum below (I taped on a steel brake line for another situation that I was doing).

Let us know how it goes!

The Medic