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As this is a delicate situation, phrasing things using "I"-statements can help reduce tension as you place the focus on your feelings. Begin with "I feel..." and state your feeling. Then, explain the behavior that led to that feeling and why you feel the way you do. Don't come into the situation and say something like, "It's hurtful that you're so flirtatious with your ex and it makes me insecure." This can sound hostile. Instead, calmly rephrase the above sentiment using an "I"-statement. For example, say, "I feel uncomfortable when you're very touchy and affectionate with your ex because it makes me feel like the two of you still have feelings for each other." After explaining your feelings, be direct and matter of fact about what you want. Remember, there is no guarantee she will be receptive. It's probably better to ask her to lessen contact or tone down interactions than demand she not talk to him at all. Say something like, "I would feel more comfortable if the two of you didn't talk as much, or if you toned down some of the physical affection, especially in my presence." Asking your girlfriend to change her relationship with someone is a very sensitive topic. It's important your girlfriend has a chance to share how she feels as it is still her decision. After making your case, let her respond without interrupting her. Give non-verbal cues to show you're listening, such as maintaining eye contact and nodding on occasion. It can also help to paraphrase what she's said to make sure you understand. For example, say, "So, you feel like the relationship is still important because the two of you were friends before you dated. Is that what you're saying?" Yelling, making accusations, calling names, and being otherwise hostile is not going to help the situation. It can be hard to stay calm during a confrontation, but take some deep breaths. Remember, you're trying to improve your relationship and not start a fight. You're talking about a situation that is occurring right now. You are not discussing the past or other issues, so do not bring these things up. This is likely to make your girlfriend feel judged and get defensive. It's very unlikely your girlfriend will flat out agree to stop speaking to someone as in this you are asking them to break bonds with someone else and this can be a large thing to ask. Therefore, you need to be willing to compromise. Find a solution where you both get what you want to some degree. For example, you could agree to let your girlfriend stay friends with her ex. She could agree to set firmer boundaries and be less physically affectionate with him. This could be a win-win situation for both of you!
Explain your feelings with "I"-statements. Be matter of fact. Give her a chance to talk. Remain calm. Stay in the present. Be willing to compromise.