Autodesk Animator FLIC animations, also known as FLC or FLI animations, are a sequence of 256 colour bitmaps shown in sequence, similar to a GIF. To save space, only the pixels changed since the last image are stored in the new image. (There may also be RLE compression in there, I can't remember).
FLC files are mainly used in some types of computer games, due to the ability to draw FLC files very quickly and compatability with some libraries, such as Allegro. Elsewhere, they are not common due to the low quality image (from the 256 colours) and low compression rates.
Programs like ASE can create and edit these files easily.