Well, regarding the apple cider vinegar treatment... I have been looking around on the internet for any studies that independently verify ACV as a treatment for varicose veins, and I haven't seen any independent studies using a double blind placebo control that back up ACV for varicose veins...even in a preliminary study,

And to add one natural remedy that DOES have some clinical backing... horse chestnut has been independently tested and the results have been promising: 5 clinical trials have shown it to be effective in reducing or eliminating varicose veins.
If anyone is interested in the studies or recommended dosage, they can check out: http://www.herbalremediesthatwork.com/horse-chestnut-herb.htm