Both females were competing for Ian's amorous attention.

The operative word is short, while to flirt, according to my dictionary, means "to pay amorous attention to without serious intentions or emotional commitment."

Peter was also the only man Sax had ever seen who did not respond to Jackie's amorous attentions in any way.

"I'll just have to put up with their amorous attentions and try to turn it to some benefit."

Sabrina was wounded, and the last thing she needed at the moment was his amorous attentions.

Seeing the object of your amorous attentions sliced up cubistically?

The Lady which attracts the amorous attentions of the passionate pilgrim.

They didn't know that he had turned his amorous attentions from Lily to her friend Catherine.

Except for his amorous attentions, Cord had mostly ignored her since the day they were wed.