on the rim, i think you need to have a lot of air and an accelerant for the rubber to burn. off the rim provides air access to the rubber. and the inside of the tire provides a place to put an accelerant.

now, if you had a large fire going already, and had a deflated tire, tossing it on top of the fire might be enough to get it to burn.

but i would still try to place the tire on top of something on the fire - in other words, i think you'd want to set it afire - like a barbeque.

in that case - on the rim - i think you'd need to heat as much of the surface area as possible to get it burning.