How to incorporate quick soaked beans into a simple vegan chilli recipe
I would soak the beans for several hours, or overnight; discard the soaking water. Tinned beans have been cooked, so place the soaked beans in your usual cooking vessel and add fresh water to about an inch over the beans. You could add in your tomato paste, spices, and cocoa powder. 

While it simmers for about 20 minutes or so, I would separately saute your onion, garlic, and mince before adding that mixture to the pot, along with all your other veg.  Simmer for an additional 10-15 minutes. You can always test a few beans, to make sure that they're becoming tender. 

You might try the white kidney beans first; they're very commonly-found in many chili recipes, but any of your bean varieties would work. Some may need shorter soaking and cooking times; the package directions should guide you in this.