Sludge in Coolant Tank in 2011 Aveo LT

I checked out my coolant on a whim when changing the headlight bulb in my 2011 Aveo, and saw that it's full of this tan sludge and I'd like to do a coolant flush myself without spending the money to have it done. Does anyone have any input?
The general idea I've gotten so far is to drain what's in there, and I'm guessing while it's empty to wipe out any sludge in the tank that I can reach, close up the drain underneath, and fill the tank to the top with distilled water. Then leave the cap off of it and fill it to the top, and run it with the heat on high with the cap off. Do I just wait until it's cool and then drain it again, or do I keep filling the tank as it's running?
Also, is this even the best way to do it?

I'd definitely flush the coolant system, but I'd be more concerned about a head gasket failure. Tan in the coolant could be oil seeping into it. More importantly, this means you could mean you have coolant in your oil which can damage your engine.

Update: The sludge in the coolant tank was caused by the "engine oil cooler". There was a leak inside it, which lead to the oil/coolant to mix in the coolant tank and produce a tan sludge. I had the engine oil cooler replaced, and it solved it. The place I went to had a $100 labor rate, and the cooler itself cost about $150 when bought by the shop. I get a discount on labor so it's $80/hr, and therefore the total that I paid was $503. This may run a bit higher depending on shop rates, but it's definitely a good thing to check out if you notice buildup in the tank!