Flippantly is how you do or say something when you are not being serious about a matter other people think you should treat with care. It describes the manner: the light tone, the quick joke, the shrug in the voice. 'He answered flippantly' means the answer itself might even be true, but the way it was given refused the weight of the question. The word is a little formal. In speech, people more often say you said it like it was nothing, or you were joking when you shouldn't have been. Used this way, it almost always criticises. You can laugh with someone and still be kind; to speak flippantly is to laugh past them.