Is there a way to duck the audio of a video track, (or, perhaps, a separate audio track), when another audio track rises above a certain level?

Automatically, no, as I know. But you can do this manually with the filter volume by keyframes.

you can also do ducking in Audacity if manual editing is too much work.
Once you have your final edit in Kdenlive, export each of your audio tracks separately as 48KHz WAVs by muting all other tracks.
In Audacity you can use the Auto Duck effect to achieve what you want, then export from Audacity as a single 48khz .wav.
Make a copy of your original Kdenlive project so you don't lose your work, and replace the audio tracks with this new track before exporting your video.

emmmm... sorry to be a bit late about this.

I found recently how to make a kind of autoducking with only one effect applied to Master Channel and two volume adjustements.

Having Two tracks that we will name Track A and Track B .
Track A (The ducking one wich will make channel B to lower volume)
Track B, (The ducked one that you will listen in background when A sounds).

All you need is to apply "Compressor/Expander" in Main Track audio effects stack with default settings.
Then in the Audio Mixer lower the Track B volume to much lower than Track A.

In my test i used 0.0db to Track A, and -13.6db to Track B. Because both input tracks where already with compressed audio .

I found that with default settings The compressor Expander Effect is able to maximize volume even when the audio (from B) is at low volume. So when when the TrackA sounds it has a new reference and makes it like trackB is in background.

Depending on how you need to acomplish this i recommend to create a separate project because changes in Main Channel Audio Effects Stack will be applied to the rest of project .

wow djquano , this is nice!!! can you do a video tutorial about ?