That story has long since been dispelled here in DK.
Frederik was photographed in public place among identified friends. During a considerable period of time, Frederik and the other friends on the boat was chatting and having a good time together, as friends tend to have.
The tabloid, Ekstra Bladet, came up with the story that Frederik was flirting with a "mystery brunette" and to back that up they produced a picture of Frederik and the woman in question.
Now, there is a TV-programme on TV2 in DK, called Presselogen, where various chief-editors discuss press-ethics every Sunday.
The then editor-in-chief of Ekstra Bladet, Bent Falbert, was thrashed by the other editors, who also had access to the picture and they pointed out that the picture had been cropped, that the presence of other firends right next to them had been ignored and that the ID of the woman had been omitted in the story in Ekstra Bladet.
Bent Falbert was litterally ridiculed when he attempted to explain the story as a good natured prank.
So, no flirt, no scandal. Just a question of picking the right picture and cropping it to suit the story you want.
The only thing the magazines accomplish by printing such stories, is to sell more magazines while discrediting themselves even more in the eyes of the readers.