There's no danger in having an occasional piece of grilled steak or blackened fish.
Theoretically, anyone who eats a lot of blackened or grilled meats could have a problem because of potentially carcinogenic (cancer-causing) compounds that form on the surface of the food, but you'd have to eat an awful lot of burned, blackened food over a long period of time for that to happen.
In another case, traditionally blackening is a southern style spice blend that imparts potent flavor to food. The traditional definition does not mean burnt food. The biggest worry should be indigestion.

