My method would be to disconnect hoses at both the cooler and block, remove the cooler from the car, flush all with mineral spirits followed by compressed air (repeat as necessary until clean/clear). Then refit cooler, attach lines to it and introduce oil into one line until you have it coming out the other one and reconnect all. Start 'er up and check fer leaks.
Admittedly potentially messy, but that's what works for me. /ubbthreads/images/graemlins/jester.gif