I guess they're hoping we don't notice they ripped off the main character from Cloudy With A Chance of Meatballs just for this. Which they did.
The trick is not to wait for the animation to finish for the last thing you did, but constantly be selecting new cones or cone colours for the next one in the line. Of course, that's just for the first couple of levels. When you "unlock" the second set of ice cream, you can start the regular cones at the same time and hold them in reserve until you need them, and look closely to see if the ice-cream-on-a-stick is oval, flat on the bottom or dick-shaped. The tricky part was figuring out how to dip them. Just for that, you have to click and DRAG, either halfway or all the way, accordingly. It gets pretty finicky at that point.
Of course, none of these tips are necessary if you don't play the game, which I suggest you don't. There are better time-wasters on Newgrounds, and ones that might actually give you some fun while you play them. The music in this is awful, so it's best to mute it and put some music up of your own while you play.