Flushing radiator

I have a 1999 Olds Sil. with a 3.4L. I want to flush the radiator because it has the build up of the black slim build up in it. I noticed that its hard to wipe off of the radiator cap. Will it really clean it out by using a water in your hose or is there something to buy to put in it that will eat the black slim without eating the gaskets. The reason I am wanting to do this is because the low coolant light stays on for about a 1/4 mile then goes out. Took cap off after car sat for 2 days and it pour out the top. The over fill jug actually has about 3/4" over the cool line, so I know its full. Open to suggestions.