The energetic usage of fuels from renewable sources or waste material is associated with controlled combustion processes with industrial burner equipment. For the observation of such processes, camera systems are increasingly being used. With additional completion by an appropriate image processing system, camera observation of controlled combustion can be used for closed-loop process control giving leverage for optimization and more efficient usage of fuels. A key element of a camera-based control system is the robust segmentation of each burners flame. However, flame instance segmentation in an industrial environment imposes specific problems for image processing, such as overlapping flames, blurry object borders, occlusion, and irregular image content. In this research, we investigate the capability of a deep learning approach for the instance segmentation of industrial burner flames based on example image data from a special waste incineration plant. We evaluate the segmentation quality and robustness in challenging situations with several convolutional neural networks and demonstrate that a deep learning-based approach is capable of producing satisfying results for instance segmentation in an industrial environment.