Engine flush has chemicals and detergents in that are designed to strip (ok,maybe a harsh word) the old gunk away, and in doing so, can dislodge aformentioned gunk, only to have it clog up some other toleranced oil channel. It is probably not to kind on the seals either.
Completely draining the old oil away, and replacing it with synthetic is a common practice, and I am pretty sure the manufacturers (oil and vehicles) would put HUGE warnings on the bottles and engines saying not to do it if it was detrimental.
What is well known is that a lot of these 'additives' that people shove in their engines are marketing ploys, and there is no major support for the practice.
Get two filters, drain the oil and replace the filter, and then run it for a while (500 -1000km) and repeat. I reckon that would be the simplest, easiest and most practical.