There is no evidence that vinegar has the ability to remove or fade permanent hair color.
More Info: Vinegar is recommended by many stylists as a useful natural hair treatment. In general, it is said to promote shine and remove residue that is left behind when styling products are used. Because of the way that permanent hair color works, your new shade has actually penetrated into the hair shaft. Vinegar only affects the outside of the hair shaft, so there is no risk of removing permanent hair color. It may be useful, however, for compensating for the stress placed on hair during the dye process.
Vinegar may be able to partially remove or fade temporary hair color. Temporary hair color does not contain the harsh peroxide agents that permanent preparations use. This type of dye either sits directly on the hair shaft, or only penetrates into the very top layers of your hair. Temporary hair color usually lasts anywhere from 5-20 washes. Because vinegar can strip the outer layers of hair, it can cause temporary hair color to fade quicker than it otherwise would. Even so, don't expect one application of vinegar to remove a bad dye job. You must use the product over a period of time before you see any fading.
The best products to remove permanent hair color are professional preparations that are designed to undo the damage. These salon preparations can bleach out bad hair color, providing a fresh palette for new color to be deposited. Vinegar does not have the ability to remove permanent hair dye.