If you use cinnamon and cloves in chili, the cinnamon and cloves should be almost undetectable. The spice is meant to provide a warm undertone.
Realistically, if you want to properly experience it, forget adding cinnamon and add good quality chorizo. It has cinnamon, but brings a lot more to the table.
You know, I've never tried it with chili, but I'll bet it would be wonderful. I'm thinking the cardamom's going to get lost really quickly, I would probably add it once at about the middle of the cooking, and then lightly dust it again at serving for the aroma.
I honestly had no idea what was in chorizo. I had been making chili with it at home and it came time to make it for work, I stopped by the market near work and they didn't have any. I was all "FINE!, I'll make my own" and looked it up, there are TONS of variations. The one I went for was basically vinegar, coriander, cinnamon, cloves, and most of the spices I already use in chili.
One of my favorite taco shops made one that was very hot and just a touch sweet the cinnamon was forward which I didn't care for at first, but it ended up being amazing, it was also processed fine like round beef. I've been trying to replicate that for a while.