How can a spectroscopic measurement be used for rates of reactions?
Yes, Using a Spectrophotometer for example.
The best example of using spectroscopic data to track the reaction rate is using a spectrophotometer, where we can use Beer-Lambert law
Here is a full lab experiment on how to determine the rate of the reaction using a spectrophotometer:
AP Chemistry Investigation #11: Rate Law of the Fading of Crystal Violet.