Welcome to the plate chiller maintenance club!
After baking at 450F for a hour or 2, backflush again with tap water. The more pressure the better when flushing. Invert the flow a few times, to flush it all out. I mount a barbed fitting onto my faucet (or garden hose) and stick the barb into one of the wort ports and hold it down to flush it out. I use a rubber/silicone washer to create a decent seal. Easy to invert the flow by sticking it in the other side. Back and forth until it runs clear.
Then recirculate 2 gallons of a boiling PBW solution for an hour (or longer) from the kettle through the pump and chiller, and let the return dump back into the kettle through a fine mesh hop bag to catch the flakes. You'd be mazed how much more crud comes out, and how brown the PBW water gets. It cleans your whole system, pump, chiller and hoses all at the same time. Again, invert the flow a few times.
When done, recirculate or flush with water. Be careful with Starsan, it will dissolve the copper brazing between the plates. Baking sterilizes the chiller, running boiling wort through at the end of the boil for 3-5 minutes will sanitize it adequately to brewer's standards.
Be careful handling boiling liquids (esp. PBW, lye, or acids) even more so when pumping. Make sure all hoses are clamped down (I'm serious!) and nothing can spray you. Wear safety goggles or a full face shield.
I do this every 4-6 brews, or when needed.
You need to find a way to prevent hop pulp getting into the chiller. So use a good and fairly large filter (to prevent clogging) before the kettle's exit port, use a hop spider, a SS hop basket, or bag your hops. The fine hop particles that make it out the spider/bags and break matter won't clog your chiller, so they can pass through.
I'm now bagging my hops, but looking for alternatives again to make life easier. I have the inkling that hop extraction suffers quite a bit from being restricted and not letting them swim freely. I really like the efficiency and speed of the plate chiller, but keeping hop matter out has been, and still is, a chore and a half. I'm considering alternatives, such as a counterflow chiller or a large immersion chiller. Then I still need to filter the wort before it goes into the fermentor as I hate having trub in there (huge loss of beer, and impossible to harvest clean yeast).
