OK, where are you in the game currently? if you're in the school, then you will find Dux if you walk up the stairs to the right and through the door at the end of the hall
If you are in the dorm and haven't gotten to the school yet, then you'll need to talk to Chance.
I'm stuck at the same part. I've got my amulet and talked to Sunflower and got the petition signed and he wants me to talk to Dux but I've gone to every available area, spoke to every person I can and clicked on everything that can be clicked on and I still can't find Dux anywhere.
Where do I find that? I've tried the school, dorm and the portal island but the only other place I could see on the map, above the others, couldn't be clicked on.
Try clicking on the book at the top of the UI. I think you may be stuck on a mission, so check if there are any of the missions there that have something you can do.