I know that someone cannot eat milk immediately after meat and vice versa. Is it ok for two people to kiss if one person has just had meat and the other has just had milk? Do they, perhaps, need to wash their mouths beforehand?
I can't imagine there being an issue as a person's mouth isn't yad soledes bo and is therefore unable to transfer flavour to another mouth.
If there is food stuck in between the teeth of one of the participants, I cant find a clear answer, however, there is an opinion that food stuck in someone's mouth after some time doesn't have any taste. The opinion is used to justify not restarting counting after meat if food is found stuck between the teeth. It could apply here to. Note, there are those who disagree.
Rav Belsky in Shulchan Halevi 22:2 p. 208 writes that a small piece of food stuck in one's mouth after some time doesn't have any taste and doesn't require restarting. He didn't want to establish at what point this would be the case.
At the very most stringent, both of you should eat a piece of bread, and bench. Beyond that, don't give it another thought.
Must one wait after a dairy meal before eating meat?
After eating dairy, one can eat meat so long as he does the following: 1. cleanses his mouth, 2. rinses his mouth, and 3. washes his hands. Some also have the practice of reciting the necessary berachot after the dairy meal, waiting, and then reciting new berachot for the meat meal. The need and permissibility of reciting berachot in this case is a subject of halachic controversy. One may clean his mouth by eating or drinking something pareve. Any solid pareve food other than dates, raw flour and greens can be used. Steps 1-3 may be done in any order.