People who live gluten free are always concerned about how their food is prepared, even when it is cooked on an outdoor grill. They need to be concerned about the food itself and also about how that food is prepared. The charcoal used in grilling can have an important effect.
Be wary of charcoal in which all the pieces have the same shape. This occurs when tiny chunks of charcoal are bonded together to improve their appearance and their ability to burn. The glue that bonds these tiny pieces together may be toxic to people who have gluten issues.
Using gluten free charcoal is the simplest way to avoid possible contamination. If that is not feasible, use charcoal that does not include any possibly-toxic ingredients.