What is it to flirt? Do you have to intend to flirt with someone in order to count as doing so? Can such things as dressing a certain way count as flirting? Can one flirt with an AI character? With one's own long-term partner? With an idea?
The question of whether or not an act of flirtation has taken place is often highly significant in our practical decision-making. For example, one may want to know whether or not one's partner has been flirting with other people in order to decide whether to continue the relationship. Or one may want to know whether two of one's friends have been flirting with each other in order to decide whether to give them some time alone. To facilitate such decisions, it would be helpful to have a secure grasp on what flirting actually amounts to.
Is that really true? Surely what's significant here is the underlying behaviour, not whether it falls under our concept of "flirting". If you're wondering whether to give two friends some time alone, presumably you should consider their desires, as reflected in their behaviour; I don't see what's gained by consulting your linguisitic intuitions about how to describe their behaviour. You know, "a rose by any other name..." and all that.
Of course, if you're interested in exploring a concept for its own sake, I have no objection to that. I'm merely puzzled by how it could prove "helpful" in any broader sense, since as a general rule only extra-linguistic facts have practical significance, right? (It can be theoretically useful to clear up conceptual confusions, of course, but that's a different matter.) When we care about flirting, i.e. the behaviour actually referred to by the word 'flirting', it's the behaviour we care about, not how we refer to it. (If it turns out that 'flirting' actually means something different from what we thought, that shouldn't change how you treat your friends!) Or am I missing something here?