I have the same setup, a whirlpool kettle and a Therminator. No filter in kettle. I bought an inline filter canister from Brewers Hardware but it clogged immediately and I never found a way to make it work. After trying about 5 times I gave up and run the whirlpool for about 15 minutes then let it settle a bit before pumping through the chillers.
That said it take a lot of work to get the chillers clean. Even after backflushing with hot PBW and a good pressure rinse, I got a glob of nastiness come out at the end of this last brew session that must have been in there for weeks and survived the cleaning and backflush. Yuck, but I ran boiling water through the chillers before using it, so at least I hope the glob was a dead glob when the beer was running past it
My previous kettle had a false bottom and that really reduced the debris going to the chillers but it could also have a problem with slow flow. A load of whole hops and some recirculation before running wort to the chillers actually had me running some really clear wort to the chillers.
I have yet to find the best of both worlds with the plate chillers and my current system. I’m thinking maybe a counterflow is in my future