Flirtatiously is how someone behaves when they are, on purpose, trying to attract sexual or romantic attention: looking, teasing, smiling, touching a little more than a plain hello would need. It names the manner of the act, not a whole personality. A person might glance flirtatiously once and then be perfectly ordinary. The word is a bit literary; in everyday talk people more often say she was flirting or he said it in a flirty way. Like flirtatious, it can be playful in a story and sharp in real life, because the same move can feel fun to one person and unwanted to another. Consent sits under this adverb even when the sentence looks light: how you look at someone is still something you do to them.