The hint for FormatConvertedBitmap gave me the solution to my problem! Thanks RononDex!
FormatConvertedBitmap convertImg = new FormatConvertedBitmap(img, PixelFormats.Bgra32, null, 0);
JpegBitmapEncoder encoder = new JpegBitmapEncoder();
encoder.Frames.Add(BitmapFrame.Create(convertImg));
encoder.Save(stream);