Before I got my pump, I would gravity feed some cleaner (PBW or oxy) through the chiller. I let that sit for a while then at the sink with garden hose, flush the chiller both directions with hot water. I then used compressed air to blow the water out, flush again, blow again ect... A lot of gunk comes out with the compressed air.
Now, with a pump, I circulate cleaner through the whole system for a while but still use compressed air to blow the chiller out.
edit - sanitizer can be gravity fed through before your wort.