I would be more concerned with the possibility oil is mixing with coolant, meaning a problem with the head gasket may exist. If that gunk is in the radiator it's throughout the cooling system. I'd check it with "Block Tester" or run a pressure check on the cooling system, or even a compression test on cylinders, in addition to flushing cooling system. You also may have a transmission cooler built into your radiator, and a leak there can allow tranny fluid to mix with coolant and result in sludge. Another possible source of sludge is mixing incompatible coolants (like red and green). If you do flush yourself, try to use deionized water, it won't promote rust like tap water. Finally, it's always a good idea to replace all coolant once every couple years, as it has rust inhibitors that break down over time.