Thanks, everyone who's responded! So, it sounds like a side-chain can be linked to any effect--not just volume, but also compression for instance. Is that right?
The source of confusion is that it is frequently called "side-chain compression" because compression is the audio effect that is used to do it in Ableton Live. In Renoise, for example, it's called Send-Receive Ducking.
It can't just be linked to any effect... if you wish to side-chain an effect in Ableton, you'll usually have to create a group with a wet channel, with your effect followed by a side-chain compression to duck the effect, and a dry. This is a really nice way to implement some effects since you'll only really get the effect when the sound quiets a bit... like, delays and reverb that are only there in the silence so they don't muddy up your sounds.
Essentially if it sends a signal you can either sidechain it or use it to sidechain. If you are using FL a quick way I learned via Varien is using Fruity Peak Controller on a clone of whatever you want to have focus for (your kick drum for example) That will make it so the sound is inaudible but it still sends a signal. Then use a Stereo Enhancer on the channel ofwhatever you want to duck out of the way in the mixer and "link to controller" and connect it to the peak controller.
what this does is that whenever you have that silent kick signal happen (most likely same time as the audible kick) whatever channel has that stereo enhancer will lower its volume and "duck" out of the way of the kick as long as that signal is still being sent. boom you've just sidechained.