1. What gauge is reading "220"; and is that gauge accurate? If the gauge is faulty, you may be chasing a problem that doesn't exist while ignoring one that does.
2. I don't trust current-production thermostats. I've seen too many that seem "sticky"; the engine gets too hot before the 'stat opens, then it goes too cool, then back to too hot, then too cool. Takes forever for the temperature to stabilize.
3. If the radiator is old, a "flush" is not likely to remove scale, or to reattach air fins that have corroded away from the coolant tubes. Radiator may need professional cleaning or replacement. Used to be that "radiator shops" were in every town even some small towns. Thanks to cheap Chinese radiators, those guys have largely gotten out of the business meaning that a professionally-cleaned, or re-cored radiator is not a viable proposition any more.
4. If the radiator can't heat-up the airflow passing through it, the fan clutch won't get hot enough to engage. Then guys install two or three fan clutches, giving up in disgust at the high number of "defective" fan clutches.
5. Every vehicle I've done radiator or A/C work to in the last number of years has had an ENORMOUS amount of dirt caught in the air fins of the radiator and the A/C condenser. I've blown amazing dust-clouds out of those heat exchangers using compressed air; it might be that a garden hose would clean 'em out also.
6. If you're going to flush the radiator, drop the coolant drainplugs on each side of the block. Kinda guessing you have a plain pipe-thread plug on the left side, and the knock sensor also plugging the coolant drain on the right side. Be sure to re-seal and properly-torque the plugs when reinstalled. There can be a lot of rust that sinks to the bottom of the water jacket.
7. MAYBE someone has replaced the block core plugs; or installed a block heater, and left the old core plugs inside the block which also can interfere with coolant flow.