The easiest way that I'm aware of would be to use AudioData[]
and pick every nth value.
audio = Audio[File["Downloads/1_mp3.wav"]];
sRate = Options[audio, SampleRate];
spacing = N[1/sRate]
The output of this first part is going to tell us the time between data points based on the sample rate of the audio file. In the case of the file I was testing, the sample rate was 22050 s$^{-1}$, which means data are 0.0000453515 s apart. You can choose any integer multiple of this that you like. In your example of 0.001 s, $0.001 \textrm{ s }\cdot\ 22050 \textrm{ Hz } = 22.05$. Therefore, the nearest integer is 22.
(* The [[1]] after AudioData[audio] selects out only the first channel.
If your data has more than one channel, you may not
want to do that. *)
data = AudioData[audio][[1]];
timing = 0.001;
selector = Round[timing/sRate];
selectData = data[[;; ;; selector]]
This isn't the most elegant code, and could certainly be tidied up depending on what exactly you want to do with the data, but hopefully this will get you started!