This is an AWESOME and fun term in spoken English. An “old flame” is a person you used to date. This could be your ex-boyfriend or ex-girlfriend. It could also be someone you just dated casually, but weren’t too serious.
If you have a new boyfriend or girlfriend, they probably will feel a little uncomfortable with you going to meet an “old flame” even for a coffee or for lunch. Every couple is different, but I think you know what I mean.
So if you had “romantic relations” with someone in the past but now you do not, that person is an “old flame“. It’s a great term and I STRONGLY recommend remembering it and using it often. (SpeakFluentEnglish)