Well the hot coolant from the engine enters the top of the radiator, and cooler coolant leaves at the bottom of the radiator. If you pull the cap when the engine is cold, and run the engine at idle until it's good and warm, you may start to see the fluid level fluctuate. (You would not necessarily notice any "flow" at the cap opening.) If there's an air pocket, you'll notice some bubbling once the temp warms up. When the thermostat opens, there should be a drop in the coolant level.
Maybe the coolant level is too low. That would render the issues you are having as well.
You may have a bad cap. If pressure does not develop in the system, it won't perform properly. Backflushing could have let some stuff loose and possibly jammed the thermostat open. It's hard to diagnose without being there.
Did the system work fine before?