With DNA its trickier. First of all, it's too small to be seen using compound (optic) microscopes. While an electron microscope scans a specimen, so either you have to do its with a frequency way higher than any vibrations, or 'focus' on a single place to 'listen' to it (pico stethoscope). There are few further complications, such as you may burn a hole though the specimen, not forgetting that it also requires special treatment to be observed in an electron microscope.
But, I think at small scales sound is closer to buffeting (like how water is the consistency of gelatin for microscopic organisms, waves can't propagate)
Sound is a bulk movement in some medium. So there isn't a useful concept of sound when you're dealing with atomic or molecular phenomena.
If individual atoms move at all they do it at very high frequencies. So there's no bulk audible movement to amplify.
The equivalent of increasing visible angular resolution would be increasing the sample rate and slowing the replay rate. You can do this easily for audio sample rates, and with a lot of extra equipment and a bit of hand waving you can convert optical or RF sampling to audio. But it still doesn't quite map to hearing in the way that microscopy maps to sight.
If you can measure it and it's changing rates, you can transform it into the human audible range.
Edit: It would likely be more interesting to listen to the DNA sequence itself. That is possible, though so far I'm just seeing an interpretation of the dna letters into musical notes: http://www.tokenrock.com/dna_music/dna_into_music.php instead of something like raw data to pcm... Not a clean transformation.
* Spectrograms: https://en.wikipedia.org/wiki/Spectrogram
* Vectorscopes: https://en.wikipedia.org/wiki/Vectorscope
Digital audio workstations [DAWs] (used often by producers of electronic music) have lots of tools for visualizing audio in this way.
Here's an example of how some of the above work in FL Studio, a popular DAW: https://www.youtube.com/watch?v=jfnWlLS6Bqg
http://lhcsound.hep.ucl.ac.uk/page_sounds_higgs/Higgs.html
Of course these collisions don't actually make sound, these are "sonifications" of data recorded by the ATLAS detector, for some interesting events.
http://lhcsound.hep.ucl.ac.uk/page_sonification/Sonification...
https://www.ted.com/talks/michael_rubinstein_see_invisible_m...
Not sure what a "sound magnifier" might actually be. There exist apparatuses called "acoustic lenses" but I don't believe they are used for applications that might be considered analogous to a microscope. Perhaps something like a stethoscope, or just a horn (think of the horn on early gramophones) might be considered as allowing humans to hear sounds that would otherwise be too faint to hear.
The audio equivalent would be more of a sonogram than the amplifier I think you are looking for.