There is no definitive answer, as the burgers may be flame broiled in some instances and not in others. Generally speaking, flame broiling is a cooking technique that uses direct heat to quickly sear food on both sides.
This can be done over an open flame or in the oven.
Since dairy products are high in moisture, it is possible that the burgers at Dairy Queen may be flame broiled on one side, but not the other. This would result in a charred patty, and not the juicy, delicious burger that fans love.
In conclusion, it is difficult to say for certain whether or not Dairy Queen burgers are flame broiled, as the cooking technique can vary from location to location. However, based on the information available, it seems likely that the burgers are not directly exposed to an open flame.