As a courtesy you probably should run it by your friend before seeing if the ex has any interest. This is especially true if the friend is one of your "best friends". Generally speaking if they only had a brief fling or your friend is the one who dumped their ex then it's probably not a big deal especially if it has been a while and the friend has found new love. On the other hand if your friend was the one who got dumped it may harbor resentment towards his ex and would be uncomfortable if you found love together or you were bringing the ex around.
One of my best friends dated one of exes and I had no problem with it. However it was not like I was ever "in love" or emotionally invested with that woman and they started dating a couple of years after she and I went our separate ways. We even had a few double dates with my new girlfriend at the time and everyone got along. We were in our mid 20s and simply enjoying life.