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?
אם כך, אם אתם אוכלים באותו הזמן היא חלבי ואתה בשרי ובהיותכם שמחים חשקה נפשך לנשק אותה, נקה את ידך ושטוף את פיך לבל יגע האוכל הבשרי בפיה ואולי תאכלנו ובזה תצא מכל החששות והספיק ספיקא הגם שהיא אינה אוכלת אותך, ואתה לא אוכל אותה וממילא כדרכם של המדיים והפרסיים ראוי שתנקה את עצמך לכבוד אשתך זו השכינה.
ואם כבר עשית מעשה ונישקת אותה מבלי שטוף פיך סביר להניח שלא נכשלתם באיסור בשר וחלב שזהו ספק רחוק ביותר. ולגבי המתנה ושהיית זמן של שש שעות בין נשיקה לנשיקה היות ואין כאן אכילה אלא רק חשש נגיעה אינך צריך להמתין ודי בניקיון פיך וידך ואין לך להמציא הלכות המתנה חדשות אשר לא שערום אבותיכם ואמותיכם.
if you are eating together, one dairy and the other meat and you get so happy together that you wish to kiss, you should first clean your hands and wash out your mouth to avoid any doubt, even though you are not eating each other, but to avoid any doubt and you should be clean like the custom of the Persians to honor your wife.
And, taking it further, if you went ahead and kissed, without washing out your mouth first, the issue is very doubtful and it is likely you have not transgressed the laws of milk and meat together. And being that there is no eating involved when kissing, the concern of waiting 6 hours after the kiss is not relevant - with touching meat and milk you just have to wash off the surface, so wash out the mouth and hands, and new laws do not need to be formulated.
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.