I figured it out. The blinking is caused by the white background layer that is automatically created by Paint.NET for new images. I forgot to delete it when making the animated GIF. When viewing the image in Google Chrome, the image appears on a black background so it was really easy to see the white rectangle flash. After I deleted the white layer, the flicker was gone. Also, BoltBait was right about the first and last frame should not be the same or else there will be a visible delay in the animation.