Machine shops normally have the facility to clean engine parts, it's basically a large tank designed to house heads and blocks with some strong solvents. I normally have the head sent there before I do porting work and then again after the head is skimmed to get rid of any swarf or metal filings.
The whole engine was clean after I got the parts back from the machine shop, all the channels in the entire engine were clean. I'm also skeptical about off the shelf engine flushers, I question their effectiveness, it might remove some grime but just because the oil looks cleaner doesn't mean there isn't still carbon build up that it couldn't remove. Only way to know for sure is to see with the whole engine in pieces. There are limits as to how strong the solvent used in off the shelf flushers, otherwise the engine would effectively be running on water while the flusher is in there and the seals would be damaged.