Catherine feared, as she listened to their [Henry Tilney's and Mrs. Allen's] discourse, that he indulged himself a little too much with the foibles of others. “What are you thinking of so earnestly?” said he, as they walked back to the ballroom; “not of your partner, I hope, for, by that shake of the head, your meditations are not satisfactory.”

Catherine coloured, and said, “I was not thinking of anything.”

“That is artful and deep, to be sure; but I had rather be told at once that you will not tell me.”

“Well then, I will not.”

“Thank you; for now we shall soon be acquainted, as I am authorized to tease you on this subject whenever we meet, and nothing in the world advances intimacy so much.”

That sounds like flirting to me, or else it is making fun of Catherine (who is more artless than artful), which would not be nice unless it was because he genuinely liked her.