I was waiting to see if anyone knew about that herb, but I don't think so.
The thing with natural healing is that is not an overnight wonder, such as surgery might be, it takes time and dedication to a certain diet and a changing of the overall lifestyle, plus being in touch with your body and overall health. I'm sure you probably know all that.
If you went to see a naturopathic doctor, they would do an overall body check and ask a lot of questions to find out where you stand physically. Information they would need to know includes your blood pressure, are you over or under weight, your thyroid condition, your normal bowel movement regularity, your daily normal diet, eating times, water intake... All these things contribute to the problem. Then you would need to discuss changes to make overall in your diet, schedules, etc. Then you'd discuss the specific problems and what to do with them, for how long and how often, what specifically you need to include in your diet for that problem, and what you need to remove.
The healing process itself takes time, but in this case, with a bigger sized kidney stone, my personal advice would be you should see an actual naturopathic doctor for help in getting rid of it.
When I read my herbal studies, I seem to remember that kidney stones can be gotten rid of with a diet of parsley and dandelion root supplementing, along with lots of water, but I know this takes time, time for the supplements to work on the stone and break it down, and if it's gotten big, then it may take even longer.
So, I guess you would have to decide how dedicated you are to really going fully with natural healing, to invest both the time, the money and the committment to stick to the diet. Surgery would be the easier way, and most likely won't kill you, but it would solve the problem quicker. But it only would focus on that problem of the immediate stone, not on your overall health and physical situation, plus avoiding the problem in the future.