I use a hose adapter to the top radiator hose with 1/4" port for compressed air. 1 1/2" PVC or iron pipe is about the right size for the radiator top hose. Pull the stat, hook the top hose up to the engine and water hose adapter and let the block fill full. Then turn the air on and blast the water and crud out. Repeat until it is clean.

This is a homemade version of a setup a saw a radiator shop use once.

I'll add I once used a strong cooling system cleaner per directions. It helped some with cleaning but I spent several weeks after fixing leaks. It was hard on seals and gaskets. Since then, water and air only for me.