When to clean 6mm CM?

When accuracy falls off. If you routinely track and monitor groups. Likely 3-400 rounds

I prefer to time mine around matches so it doesnt go in the middle of a match. Especially a 2 day since I wouldn't have much of a way to refoul it and they matter a little more
 
I clean mine when groups open up or SD/ES gets suspect. Most of my barrels have gone 600-700 without cleaning before I chickened out and cleaned it, but I currently have one that's needed regular cleanings every 300-400 rounds to keep it from getting a bad carbon or copper ring that wrecked my SD/ES. One decent cleaning later, everything was back to normal.

Your rifle will tell you when it's time.
 
I normally clean mine every 300 or so rounds or before a 2-day match. Put 10 or so rounds through to check zero and MV after cleaning and it's good to go.
 
I've been running an oily patch or two down the bore after every match and hit the road. Once home, a couple dry ones, 3-5 hours later. No issues. After I passed the 700 mark a copper cleaned and rechecked my velocity, which has remained unchanged after the second round fired.

This bore has only seen coated 115 dtac's and very little copper was seen on the clean out patches.

With the aid of a borecam, I have not seen any evidence of carbon build up and only traces of copper.

Cold clean bore with 2 shots each of three different load sessions spanning 7 weeks for a total of 6 shots.
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So many variables there is no one answer. Let the barrel tell you via group size with a known control load.
Powder type can have a large effect on cleaning frequency; my rifle running AR2209 (H4350) seem to require
a lot less frequent cleaning than slower, dirtier powders.

EDIT; just saw Niles test above , interesting. Ive had some barrels that seem to last forever, and others that died too soon.
Another variable....