I agree- there is no need to avoid Amsterdam on Kings Day. I was there in Amsterdam on Kings Day a few years ago. I put on my orange shirt and set out walking at 9:00 am from my hotel. The streets in the central ring were shut down or diverted, so walking was a breeze. For the first hour, there was barely anybody outside. It wasn't until 10 am that people brought out their items for sale on blankets in the street. Only around noon, did the city become crowded - and then only in the areas that were hosting events. The ferry across the river was crowded and Dam square was crowded. Around 2 pm, the canals in the Jordaan were full of boats with revelers all wearing orange. Quite a party scene. But other than that, it was not wall to wall people. Honestly, I was a bit disappointed in the crowd size. I thought it would be like Times Square on New Years eve in New York or Spring Break in Fort Lauderdale or Miami Beach throughout the city. But it wasn't that crowded. And in the event areas where there were crowds, the people were respectful. It wasn't a mad house.
I wouldn't avoid Amsterdam for fear of crowds. Put on a orange shirt and enjoy the festivities.