Depending on your Mac, it may be as simple as connecting the Kindle headphone socket to the Mac Stereo Line-In with one of these.
The Line-In on a Mac looks like a thin circle with two black arrows.
If you have no such thing, then look at Apple > System Preferences > Sound and see if it lets you switch one connection between headphone and Stereo Line-In.
Failing that, you should get one of the many fine Stereo to USB adapters. I use the Behringer UCA202.
It works with many different computers.
For that, you’ll need a different cable.
Launch Audacity and use the Device Drop-Down to switch to “USB Audio Codec.” If that listing isn’t there, restart Audacity and try again.
Hearing what you’re doing can be a challenge because you just used up the headphone connection on the Kindle and that turns off the speakers (if any).
You can set Audacity to play what it’s recording to your speakers.
Audacity > Preferences > Recording > [X] Software Playthrough. Only select that.
I’ve never actually met a Kindle, but I’m guessing it works like other portable media players.