Low pressure air is correct for flushing out lines and coolers.
Disconnect the cooler lines at the C6 and using a rubber tipped nozzle blow the crud from the cooler. Put a rag over the exit tube so you do not blow the crude into your eyes. Now flush out the C6 by running the engine and letting the return line exit into a clean bucket.
IF YOU DO NOT HAVE LP AIR:
Get a garden sprayer, cut off the spray line, make an adapter for the cooler line and using tranny fluid, pump it up and blow out the lines and cooler.