It's not uncommon for ex's to flirt with one another. This can be a way to show that there are no hard feelings, or it can be an opportunity to suggest that there's an interest in getting back together. Flirting with your ex-girlfriend can be like flirting with somebody new, although there are certain elements of your flirting that can reference your previous relationship in a positive way.
Every couple has jokes that exist just between them. It's unlikely that your ex-girlfriend would've shared these private jokes with anyone else, so referencing one while flirting can be a nice way of bringing up a positive and playful element from your time together. Ideally, you should incorporate inside jokes into compliments. For example, if you used to joke that she always felt chilly when walking outside, you could say (with a smile), "Lovely jacket. Though, let me guess, you're feeling cold?"
Reference Positive Things From Your Past.
Every couple has favourite memories that they share. You can draw on these during when flirting after your break-up. You can be playful or more suggestive, depending on your style, the sense of humour or your ex, and the level of comfort between you. For example, "That smile brings back memories" is a considerably more lighthearted comment than winking and saying, "I remember seeing that dress thrown across my floor..." The latter remark is substantially more provocative. Whatever the case, make sure that your comment is appropriate, you do not want to offend her.
Surprise your ex with the occasional text, e-mail or letter. Spontaneous flirtatious messages can help to keep you in her mind and can let her know that your interest surpasses the occasional remark made in person. These don't have to be complex. They can be complimentary and should be just enough to arouse her curiosity.
Teasing is often an element of flirting, as it demonstrates confidence and suggests that you feel comfortable enough with her to make jokes at her expense. Again, draw on your romantic history to incorporate a few good-natured taunts into your flirting. For example, "I see you can finally fit into your favourite jeans."