Well, I don't 'clean' my chain, per se, but just wipe it off with a rag.
Always do it with the chain warm, after riding 60kms home from work.
I have used Maxima Racing Lubricants Chain Wax (pic below) for the last several years.
Ride home, wipe the chain, squirt the Chain Wax in between the o-rings, wipe any excess (if any) off, let sit for 30mins to 'set up'.
Absolutely no fling, and I do this every 500kms - 800kms (I use tip meter 2 to gauge this)
My chain is as clean as the day it was fitted, as the wax doesn't attract dirt as it's essentially 'dry'.
I have tried the *new* and *improved* teflon product from the same manufacturer and the bloody stuff flung off EVERYWHERE!
So, I figured, why re-invent the wheel - use what I know works, and my chain is now more than 30000kms old (to be fair, 20000kms of that was with the previous owner), and still well within the adjustment specs.
Cheers,
Rick