>>1990555I usually just capture the screens from a video player and import them as frames into Photoshop. Diffusion dithering looks like the best way to go in terms of reducing the colors as it seems to fare best with gradients, such as the one in Kirino's hair as well as the blush on her cheeks.
There are few optimizations that I usually do to them in order to reduce the file size as well, but they have to be made by hand frame by frame so it can take a significant amount of time. However, it can cut down the file size a lot, especially on gifs that have large areas of static background scenery and can be useful in avoiding the 3 MB file size limit on /c/.