Here's the Thing…
Dating your ex’s friend is fraught with danger. There’s nothing about it that will make things better with your ex—and many things that can make them worse.
There’s the possibility of your ex-girlfriend—whom you can expect to hear about more than you would otherwise—sabotaging your new relationship. Of course, there’s the chance that your old and new girlfriends won’t stay friends—but remember, she’s already heard all of your ex’s complaints about you.
At first this doesn’t matter much. Her friend thought about all this before she decided to date you. But it can matter down the road, when you and your new girlfriend are fighting about something and she brings up similar things you supposedly did to your ex.