I’d recommend finding a local shop that has a powered flush system. They hook it up at the upper radiator hose block and radiator connections. It might take more than 1 visit to get all the gunk out. After the first flush replace the coolant in the overflow tank (if not super clean) and make sure the plastic dip stick is well cleaned too. Monitor the dipstick over time for signs of rust coloring - let’s you know whether another flush might be needed?
If not too bad, for 2nd go around could just drain radiator and refill then repeat 2 more times after a few months of driving.