The description of the Burning state explicitly says that unlike other states a character may have more than one burning token at a time. The new characters that use burning have switches in their attacks that can place burning tokens. For instance Kosmo's Supernova Attack has a switch that allows him for the cost of he may place a burning token on each adjacent enemy. If he rolls , may he place two burning tokens on each enemy? Likewise on Mendoza's Attack Flamma Veritatis for the cost of he may place a burning token on the target, again if he gets , may he place two burning tokens? Mendoza'a Action Deus Vult if successful imposes a burning token on all adjacent enemies but does the switch of cost allow for extra burning tokens to be placed within 1-2?
You can activate the same switch multiple times as long as you can pay for them. So if you can activate Kozmo's switch multiple times, that is how many burning tokens he will dish out. Mendoza's Flamma Veritatis attack seems like its meant for you to decide whether your attack do hits or hand out burning tokens to your target. As for Deus Vult, it only puts out 1 burning token within the 1-2 range per switch, not repeating the actions ability of making all targets within 1 get burning. I think the real question about burning is if you are limited to the number of tokens you can give out by the supply you have.
Flamma Veritatis can deal "damage" even if the opponent rolls shields by just converting your to burning tokens. It's good for killing tanks.