Sounds to me like sludge from dexcool? I've never seen a block that has been flushed continue to pollute antifreeze, no matter how bad.
If it's this nasty, fill it with water, run it, and drain it until the water stays clear, then refill with antifreeze mix.
The cooling water system is a closed system. If you are getting large quantities which look like mud, I suspect you are still getting residual rust that was trapped inside the system. In other words, your initial flush must have left some debris in the system. When you flush, make sure you are flushing through your cars heater circuit as well. It is also tied to the cooling water circuit.
Rust is caused by the oxidation of iron. Your engine block is cast iron and there are other iron components in the circuit. The radiator fluid has a rust inhibitor in it as well as the antifreeze. Once you get all the accumulated rust off of the engine cooling ports, you should not be seeing large accumulations of "mud" in the system. It is possible there is scale on the walls of the cooling water circuit which did not come off during the initial flush but was loosened and come off during the second flush.
Give it a real good flush all the way through the engine block. Make sure you're not flushing the mud into your radiator where it can get trapped in the radiator pores.
Good luck!
Woops, Flushing will not remove corrosion and rust! GM makes an inexpensive *one part powered acid cooling system cleaner that will do the trick. Follow the instructions on the back of the bottle for best results. Make darn sure the cooling system is clean and empty before you drain the block before the next step. Read the specifications pages on the glove compartment manual to see what the total capacity of the cooling system is. Fill the cooling system with 1/2 it's total capacity first, with the correct GM recommended 100% full strength antifreeze. Fill the remaining space with distilled water from any grocery store. Take time to remove the plastic coolant recovery bottle and clean it out with Wisk liquid soap and a stiff round household scrub brush.
Its a 94 Chevy s10 blazer. I got the car from an older gentleman. Just about everything on it was original. About 2 years ago we changed out just about the whole cooling system (thermostat, water pump, a brand new radiator and hoses etc) and had it flushed a few times but the rust comes right back. It looks like someone just dumped mud in it. I'm very meticulous about maintenance So I've always added all the correct fluids. There is no visible leak and no oil is mixing in it.
What else could be causing this. I'm going to get it flushed again this week.