No, flipX and flipY properties don't make a lot of sense for a bitmap. Bitmap files are device independent formats that store raster 2D graphics—it contains pixel data. You can display it however you want; why should that information be embedded into the file? None of the file structures you linked to contain such properties.
Use the Image.RotateFlip method to change how it is displayed.
Whose implementation of the .NET Framework are you interested in? Microsoft's? It uses a Windows bitmap, defined either through a BITMAPINFOHEADER structure or the extended version, BITMAPV5HEADER, all carefully documented here.