And I am speaking of in-show shipping, not fandom shipping where any character can be paired up with anyone including nevermet shippings.
Even though its still very early, I doubt Iris or Dento will have any shipping subplot in Pokemon. Dento is already a ladies man but goes no further with it, and Iris just seems like the kid to be uninterested in romance altogether.
Likewise Dawn seemed completely oblivious to romance, and in a way only focused on her Pokemon/battles, similar to Ash. We know both Conway and Kenny definitely liked her, but the first was mostly played for lol's and Kenny just got a, "We'll be friends," kind of message to it.
Do you think the writers have moved away from shipping amongst the main cast?