Are you talking about the bottom sole or midsole? If you are talking about the bottom sole, then I would recommend not painting it. If you paint the bottom sole the paint will chip off very quickly (faster than the original) and won't last very long. If you really want to paint the sole, then it is best to paint the sole and then seal it with sole protector (just google it). This is a lot of work, especially for a part of the shoe that not many people will see. But if you want to put in the effort then go for it.
If it is the midsole then you are going to want to strip the paint fully, and then add a few layers of angelus leather paint. The reason we use angelus is because it is more flexible than other paints, and won't chip as easily. Just youtube how to re-paint air jordan midsoles on youtube and you will get some great tutorials.
Matching the greys will be difficult, so I suggest that you buy some grey, white, and black paint, and try to match it best yourself. You can buy angelus paint at suppliers like turtlefeather.com and angelusdirect.com
Good luck!