I have used the Blichmann chillers for many years, and sometimes two of them in series. No matter what you would normally want to do, and regardless of what filter you buy, there will always be debris in the process that will get into them. Taking that into consideration I consider the end of the brew process the first step in making sure they never have issues. (notice I didn't say they were ever perfectly clean)
1. Before use I flush with regular tap water. It's amazing what comes out after the unit has sat for weeks and you swear you clean the hell out of it last time it was used. (my sanitation is hot wort circulation in the last part of the brew process, nothing else)
2. Flush with water, swap the input and output a few times and burst the water off and on both ways until minimal debris is coming out. I use a white bucket for the water coming out to see what is coming out.
3. Sometimes I may place some PBW in one of the vessels and pump warm PBW through the chiller(s) for a while (after the above water flushing). This is done every once in a while when I have spare time but not every time. Rinse with water as above after the PBW.
4. Blow out excess water and store.
I have used everything from a Bazooka screen (fail), to false bottom(best), to Brewer's Hardware filter canister (fail), but all filtration seems to have its limit and has caused issues at one time or another. I have started whirlpooling and picking up from the edge of the bottom, but frankly there is still a ton of debris in suspension that goes through the chillers this way. Regardless of the huge debris load, no issues.