Only thing about "flushing " an engine is the better
than average chance of breaking loose all the built
up sludge, only to have it severely clog the oil
pickup screen, then you are truly screwed.
Used to be when vehicles had a screen and a
sump that the screen poked down into, you could
drain the oil and refill it with a about a gallon or
two of solvent or naphtha and let it sit and soak
for a couple of days, and it would melt a lot of
the sludge and you could take the plug out and
drain it and pour more stuff through with the plug
out and the remnants would rinse on out.
I'm not sure at all about the modern OHC engines
because of their complicated oiling systems.
Not all all like an old V8 engine
Good Luck