There is no such thing as a "codec for kaffeine", kaffeine uses xine as its backend, so it all comes down to what video formats do your xine libraries support. Xine supports a number of codecs natively (a big number), and some others can be supported via external ffmpeg or lavc (and maybe some other library), so maybe installing those package can help.
In second place, ".avi" doesn't tell us anything at all about what the exact contents of the file is (other that it's a video file). ".avi" is just what we call a "container format", but not a proper audio or video format. Avi files can contain audio and video streams that can be encoded like with a million different audio and video formats.
If xine can't play your file, I suggest trying mplayer, I can't guarantee that it will play the file, but at least the output will be more valuable and can help us diagnose what the exact codecs are and if there's any chance that you can play it at all.