I'm able to create line charts, profile graphs, etc. on a feature layer, but I have to use the CIMChart classes in the ArcGIS.Core.Internal.CIM namespace. I don't see any documentation online (yay IntelliSense), and the namespace implies that it isn't intended for "public" use. The solution is built solely on trial and error.
I was informed that charting built into the Python library (Chart—ArcPy classes | ArcGIS Desktop), but it isn't currently available in the .NET SDK. We have a tool in a few ArcMap extensions that allows users to sketch a line segment, then runs LOS analysis on the segment and generates a profile graph so the user has multiple visualizations. We're trying to migrate to ArcGIS Pro, so this functionality would be very beneficial.