Hi, I'm not the most experienced flusher here but I wouldn't see it as a failure. When I did my 6th flush (I think, lose track of how many I've done now!) I threw up most of the OO/GF mix and produced no stones. I was really disheartened by this but like you are thinking of doing, I waited just a week before doing another and had my most productive flush yet. I passed a stone over an inch across and after that about 50 pea-sized stones. Perhaps the large stone was blocking the release of smaller stones? It is beneficial to have a colonic or enema after a flush for this reason.
I think it would be wise to leave at least a week before doing another flush. Even though you didn't get any visible results, your liver has undergone a detox and will need a little time to recover and build up bile again. I have started taking milk thistle supplements which are very beneficial in maintaining healthy liver function, and I think a supplement such as this is well worth taking during a Liver Flushing regime at fortnightly intervals.
If you haven't already had a colonic or been on a colon cleansing programme such as colonix, it is highly advisable as an efficiently functioning digestive system will improve liver function leading to more productive liver flushes. A parasite cleanse would benefit you too.