That's not going to remove the (infectious) pulp.Bleach may follow but I try to use as little of that as possible.
I would shake that chiller out (on each side) so it's it's as dry as it can get.
Then bake it in an oven at 450F for a few hours. That will dry out the leftover flakes, highly reducing their volume and clogging abilities, while sterilizing everything.
After the bake, if you have an air compressor, blow the flakes out. Then rinse out with water. Start with a slow flow (or recirculate slowly) to slowly flush the remainder out, without creating another clog. When recirculating, filter the output through a fine-mesh hop bag or such, to trap the debris.
When all done, re-sanitize and it should be ready to go.
I filter the wort before it enters my 40-plate chiller, Rinse it out after use and let it air dry. And bake it 1 or 2 times a year, for good measure.
I've looked into those too. The channels in those tend to be much wider than our chillers' so most pulp will pass through. Aside from the acquisition price, all the gaskets need to be replaced when reassembling them after each overhaul, which is not a cheap endeavour either.Kicking myself that I didn't buy my buddy's big huge 80-plate take-apartable chiller when I had the chance but it was out of my budget.