found in the internet:

Should you Use Engine Flush?
Engine flush is special solution that helps to remove deposits and coating from internal engine parts right before an oil change. It's useful if your engine is slightly dirty inside. But, if there is too much carbon buildup (indicated by the arrow in the photo) inside the engine, flushing may have bad effect, because washed off carbon particles may clog the oil screen in the crankcase oil pan, which may cause a lack of oil pressure.

So, how do you decide if you should use an engine flush solution? If you notice, that the engine oil becomes too dirty (dark - brown color) even in few days since you've changed it, it means your engine is too polluted inside, like the one in the image. In such case you'd better avoid engine washing off. But if you notice, that even after 2000 - 3000 miles since last oil change the engine oil remains translucent or slightly brown, it means your engine is clean inside. So, you may apply the engine flush facilities successfully.


I read between the lines that when flushing the engine you should of course clean the oil screen and also change the oil filter after that.
I don`t think that our engines look so bad inside as some car, truck or marine engine with high milage. Seen in my own engine there was rather oil sludge in it than carbon buildup. In this case engine cleaners help. One may also consider to flush the engine, then do the next oil change after a short period maybe using some cheaper oil for this. Or flush every couple of years to keep it clean. (which shouldn`t be necessary with regular oil changes)
If the engine is in too dirty condition better not flush it.