Sorry,
Define "stuck rings"
I did this flush about 20k miles ago. The only bad effect is the added use of oil.
Like I have said, I have used a different "sealer" with each oil change. Motor honey, ring seal, etc. It seems to be working to slow the leak.
stuck rings:
for what ever reason, the compression rings(there's 2 of them) and/or the oil ring may be partially stuck in the ring grooves.
the piston is smaller than the cylinder bore. it(in theory) never touches the cylinder bore. the piston rings are all that do touch it.
as the plug fires, creating pressure in the quench area, this forces the piston down. it also forces all 3 ings out against the cylinder wall. or rather, it's supposed to force them out. by doing this, it seals compression out of the crank case(for the most part), and keeps oil from getting into the combustion chamber.
if during the cleaning, something got caught in one of the grooves, they may have gotten stuck in their grooves. so, if they're stuck, the oil ring won't clean all of the oil off of the cylinder wall, and it'll end up in the combustion chamber, getting burnt.