Reply To: Should I just drop it?

Right. You should not take at face value a statement like your boyfriend gave you. You should dig deeper and have a conversation about why he would give his number to a girl he met on a plane and would have a flirty text convo. You could ask him how he would feel if you did the same. You could point out that one does not have to give one’s number to anyone, and one also does not have to respond to texts, and that you noticed his responses seemed designed to continue a conversation, not shut it down. Ask how he’s feeling in the relationship. Is he happy?

Look, BEST case here is he’s not interested in this girl or in stepping out on your relationship but he was flattered by the attention. In which case, like Anon said, shut that down. Worst case he’s open to meeting other women and you should reevaluate the relationship.