To be honest I don't know if that is going to achieve much. I have had to scrape out the water passage in the exhaust manifold, replace the mixing elbow and overhaul the heat exchanger at various times and just feel like the kind of crud that had to be removed just would not respond to flushing, but what the heck, it is worth a try.
For grins I have attached before and after pictures of the heat exchanger and also the mixing elbow showing the piece that dropped out with zero warning. The mixing elbow was surprisingly unclogged.
Good luck and please let us know how it works. Doubt the volume will be anywhere near 4 gallons.